(x-5)(x+8)=5(x-5)

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Solution for (x-5)(x+8)=5(x-5) equation: 


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

Reorder the terms:
(-5 + x)(x + 8) = 5(x + -5)

Reorder the terms:
(-5 + x)(8 + x) = 5(x + -5)

Multiply (-5 + x) * (8 + x)
(-5(8 + x) + x(8 + x)) = 5(x + -5)
((8 * -5 + x * -5) + x(8 + x)) = 5(x + -5)
((-40 + -5x) + x(8 + x)) = 5(x + -5)
(-40 + -5x + (8 * x + x * x)) = 5(x + -5)
(-40 + -5x + (8x + x2)) = 5(x + -5)

Combine like terms: -5x + 8x = 3x
(-40 + 3x + x2) = 5(x + -5)

Reorder the terms:
-40 + 3x + x2 = 5(-5 + x)
-40 + 3x + x2 = (-5 * 5 + x * 5)
-40 + 3x + x2 = (-25 + 5x)

Solving
-40 + 3x + x2 = -25 + 5x

Solving for variable 'x'.

Reorder the terms:
-40 + 25 + 3x + -5x + x2 = -25 + 5x + 25 + -5x

Combine like terms: -40 + 25 = -15
-15 + 3x + -5x + x2 = -25 + 5x + 25 + -5x

Combine like terms: 3x + -5x = -2x
-15 + -2x + x2 = -25 + 5x + 25 + -5x

Reorder the terms:
-15 + -2x + x2 = -25 + 25 + 5x + -5x

Combine like terms: -25 + 25 = 0
-15 + -2x + x2 = 0 + 5x + -5x
-15 + -2x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 5}

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