Question

Solve for x. 4x(x-9)-5x(x-8)=-5

Answer 1

4x(x-9)-5x(x-8)=-5

Multiply 4x by each term inside the parentheses.
4x^(2)-36x-5x(x-8)=-5

Multiply -5x by each term inside the parentheses.
4x^(2)-36x-5x^(2)+40x=-5

Since 4x^(2) and -5x^(2) are like terms, add -5x^(2) to 4x^(2) to get -x^(2).
-x^(2)-36x+40x=-5

Since -36x and 40x are like terms, subtract 40x from -36x to get 4x.
-x^(2)+4x=-5

To set the left-hand side of the equation equal to 0, move all the expressions to the left-hand side.
-x^(2)+4x+5=0

Multiply each term in the equation by -1.
x^(2)-4x-5=0

In this problem 1*-5=-5 and 1-5=-4, so insert 1 as the right hand term of one factor and -5 as the right-hand term of the other factor.
(x+1)(x-5)=0

The complete solution is the set of the individual solutions.
x=-1,5

Answer 2

4x(x-9)-5x(x-8)=-5
4x² - 36x - 5x² + 40x = -5
-x² + 4x + 5 = 0
x² - 4x - 5 = 0
4 +- sqrt 36 / 2
4 +- 6 / 2
10/2 and -2/2
x = 5 and x = -1