(x-5)(x+8)=8(x-2)

Solution for (x-5)(x+8)=8(x-2) equation:

Simplifying
(x + -5)(x + 8) = 8(x + -2)

Reorder the terms:
(-5 + x)(x + 8) = 8(x + -2)

Reorder the terms:
(-5 + x)(8 + x) = 8(x + -2)

Multiply (-5 + x) * (8 + x)
(-5(8 + x) + x(8 + x)) = 8(x + -2)
((8 * -5 + x * -5) + x(8 + x)) = 8(x + -2)
((-40 + -5x) + x(8 + x)) = 8(x + -2)
(-40 + -5x + (8 * x + x * x)) = 8(x + -2)
(-40 + -5x + (8x + x2)) = 8(x + -2)

Combine like terms: -5x + 8x = 3x
(-40 + 3x + x2) = 8(x + -2)

Reorder the terms:
-40 + 3x + x2 = 8(-2 + x)
-40 + 3x + x2 = (-2 * 8 + x * 8)
-40 + 3x + x2 = (-16 + 8x)

Solving
-40 + 3x + x2 = -16 + 8x

Solving for variable 'x'.

Reorder the terms:
-40 + 16 + 3x + -8x + x2 = -16 + 8x + 16 + -8x

Combine like terms: -40 + 16 = -24
-24 + 3x + -8x + x2 = -16 + 8x + 16 + -8x

Combine like terms: 3x + -8x = -5x
-24 + -5x + x2 = -16 + 8x + 16 + -8x

Reorder the terms:
-24 + -5x + x2 = -16 + 16 + 8x + -8x

Combine like terms: -16 + 16 = 0
-24 + -5x + x2 = 0 + 8x + -8x
-24 + -5x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-24 + -5x + x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-3, 8}