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

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

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

Reorder the terms:
(-5 + x)(x + 8) = 4(x + -5)

Reorder the terms:
(-5 + x)(8 + x) = 4(x + -5)

Multiply (-5 + x) * (8 + x)
(-5(8 + x) + x(8 + x)) = 4(x + -5)
((8 * -5 + x * -5) + x(8 + x)) = 4(x + -5)
((-40 + -5x) + x(8 + x)) = 4(x + -5)
(-40 + -5x + (8 * x + x * x)) = 4(x + -5)
(-40 + -5x + (8x + x2)) = 4(x + -5)

Combine like terms: -5x + 8x = 3x
(-40 + 3x + x2) = 4(x + -5)

Reorder the terms:
-40 + 3x + x2 = 4(-5 + x)
-40 + 3x + x2 = (-5 * 4 + x * 4)
-40 + 3x + x2 = (-20 + 4x)

Solving
-40 + 3x + x2 = -20 + 4x

Solving for variable 'x'.

Reorder the terms:
-40 + 20 + 3x + -4x + x2 = -20 + 4x + 20 + -4x

Combine like terms: -40 + 20 = -20
-20 + 3x + -4x + x2 = -20 + 4x + 20 + -4x

Combine like terms: 3x + -4x = -1x
-20 + -1x + x2 = -20 + 4x + 20 + -4x

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

Combine like terms: -20 + 20 = 0
-20 + -1x + x2 = 0 + 4x + -4x
-20 + -1x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 5}