Question

(y+2)^2=2y^2+y-24

solve for y

Answer 1

Expand the LHS(Left Hand Side)

Answer 2

y+2+y+2 = 2y^2+y-24

Answer 3

y^2+4y+4 = 2y^2+y-24

Answer 4

(y+2)^(2)=2y^(2)+y-24

Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
2y^(2)+y-24=(y+2)^(2)

Since (y+2)^(2) contains the variable to solve for, move it to the left-hand side of the equation by subtracting (y+2)^(2) from both sides.
2y^(2)+y-24-(y+2)^(2)=0

Squaring an expression is the same as multiplying the expression by itself 2 times.
2y^(2)+y-24-((y+2)(y+2))=0

Remove the extra parentheses around the factors.
2y^(2)+y-24-(y+2)(y+2)=0

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.
2y^(2)+y-24-(y*y+y*2+2*y+2*2)=0

Multiply y by y to get y^(2).
2y^(2)+y-24-(y^(2)+y*2+2*y+2*2)=0

Multiply y by 2 to get 2y.
2y^(2)+y-24-(y^(2)+2y+2*y+2*2)=0

Multiply 2 by y to get 2y.
2y^(2)+y-24-(y^(2)+2y+2y+2*2)=0

Multiply 2 by 2 to get 4.
2y^(2)+y-24-(y^(2)+2y+2y+4)=0

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, y is a factor of both 2y and 2y.
2y^(2)+y-24-(y^(2)+(2+2)y+4)=0

Add 2 to 2 to get 4.
2y^(2)+y-24-(y^(2)+(4)y+4)=0

Remove the parentheses.
2y^(2)+y-24-(y^(2)+4y+4)=0

Multiply -1 by each term inside the parentheses (y^(2)+4y+4).
2y^(2)+y-24-(y^(2))-(4y)-(4)=0

Multiply -1 by the y^(2) inside the parentheses.
2y^(2)+y-24-y^(2)-(4y)-(4)=0

Multiply -1 by the 4y inside the parentheses.
2y^(2)+y-24-y^(2)-4y-(4)=0

Multiply -1 by the 4 inside the parentheses.
2y^(2)+y-24-y^(2)-4y-4=0

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, y^(2) is a factor of both 2y^(2) and -y^(2).
(2-1)y^(2)+y-24-4y-4=0

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 2 and -1 and give the result the same sign as the integer with the greater absolute value.
(1)y^(2)+y-24-4y-4=0

Remove the parentheses.
y^(2)+y-24-4y-4=0

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, y is a factor of both y and -4y.
y^(2)+(1-4)y-24-4=0

To add integers with different signs, subtract their absolute values and give the result the same sign as the integer with the greater absolute value. In this example, subtract the absolute values of 1 and -4 and give the result the same sign as the integer with the greater absolute value.
y^(2)+(-3)y-24-4=0

Remove the parentheses.
y^(2)-3y-24-4=0

Subtract 4 from -24 to get -28.
y^(2)-3y-28=0

In this problem 4*-7=-28 and 4-7=-3, so insert 4 as the right hand term of one factor and -7 as the right-hand term of the other factor.
(y+4)(y-7)=0

Set each of the factors of the left-hand side of the equation equal to 0.
y+4=0_y-7=0

Since 4 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 4 from both sides.
y=-4_y-7=0

Set each of the factors of the left-hand side of the equation equal to 0.
y=-4_y-7=0

Since -7 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 7 to both sides.
y=-4_y=7

The complete solution is the set of the individual solutions.
y=-4,7

Answer 5

so,
y=-4,7

Answer 6

y=-4,7

Answer 7

yes

Answer 8

lolz @some_someone Do you know who you're teaching? Because @Rasheika is obviously not the person who asked the question.

Answer 9

Lol

Answer 10

lulz sorry, yeah @Mustakim14 answered the question. And i was agreeing with @Rasheika . sorry though.

Answer 11

And @Rasheika That's not teaching. You just rewrote the answers without any working. That's against policy.

Answer 12

How bout i just not answer any more of your questions and than we wont have to worry about the policy toodles :) @Azteck