(x-4)(x+5)=x-4

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Solution for (x-4)(x+5)=x-4 equation: 


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

Reorder the terms:
(-4 + x)(x + 5) = x + -4

Reorder the terms:
(-4 + x)(5 + x) = x + -4

Multiply (-4 + x) * (5 + x)
(-4(5 + x) + x(5 + x)) = x + -4
((5 * -4 + x * -4) + x(5 + x)) = x + -4
((-20 + -4x) + x(5 + x)) = x + -4
(-20 + -4x + (5 * x + x * x)) = x + -4
(-20 + -4x + (5x + x2)) = x + -4

Combine like terms: -4x + 5x = 1x
(-20 + 1x + x2) = x + -4

Reorder the terms:
-20 + 1x + x2 = -4 + x

Solving
-20 + 1x + x2 = -4 + x

Solving for variable 'x'.

Reorder the terms:
-20 + 4 + 1x + -1x + x2 = -4 + x + 4 + -1x

Combine like terms: -20 + 4 = -16
-16 + 1x + -1x + x2 = -4 + x + 4 + -1x

Combine like terms: 1x + -1x = 0
-16 + 0 + x2 = -4 + x + 4 + -1x
-16 + x2 = -4 + x + 4 + -1x

Reorder the terms:
-16 + x2 = -4 + 4 + x + -1x

Combine like terms: -4 + 4 = 0
-16 + x2 = 0 + x + -1x
-16 + x2 = x + -1x

Combine like terms: x + -1x = 0
-16 + x2 = 0

Factor a difference between two squares.
(4 + x)(-4 + x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4

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

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

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

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

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

Simplifying
x = 4
Solution
x = {-4, 4}

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