Question

solve by factoring.
4x^2+23x+15=0

Answer 1

Simplifying
4x2 + 23x + 15 = 0

Reorder the terms:
15 + 23x + 4x2 = 0

Solving
15 + 23x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(3 + 4x) = 0

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Solution
x = {-5, -0.75}

forgive me was afk :P

Answer 2

first note, everything is positive- no negatives when factoring
next, look at multiple pairs of 4 and 15
mulitple pairs
4- (1 4) (2 2)
15- (1 15) (3 5)

the determine if a combination/ dot product from 4 and 15 will give you 23

1*1+4*15 = 61
1*15+4*1=19
2*1+2*15=32

etc

once you find the combination, then arrange in the form of (ax+b)(cx+d)=0

where a and c were the multiple pairs from 4
and
b and d were the multiple pairs from 15

Answer 3

thanks guys (: