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

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Solution for 4x(x-9)-5x(x-8)=-5 equation: 


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

Reorder the terms:
4x(-9 + x) + -5x(x + -8) = -5
(-9 * 4x + x * 4x) + -5x(x + -8) = -5
(-36x + 4x2) + -5x(x + -8) = -5

Reorder the terms:
-36x + 4x2 + -5x(-8 + x) = -5
-36x + 4x2 + (-8 * -5x + x * -5x) = -5
-36x + 4x2 + (40x + -5x2) = -5

Reorder the terms:
-36x + 40x + 4x2 + -5x2 = -5

Combine like terms: -36x + 40x = 4x
4x + 4x2 + -5x2 = -5

Combine like terms: 4x2 + -5x2 = -1x2
4x + -1x2 = -5

Solving
4x + -1x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 4x + -1x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 4x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(1 + x) = 0


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {5, -1}

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