(x-4)(x+8)=6(x-4)

Solution for (x-4)(x+8)=6(x-4) equation:

Simplifying
(x + -4)(x + 8) = 6(x + -4)

Reorder the terms:
(-4 + x)(x + 8) = 6(x + -4)

Reorder the terms:
(-4 + x)(8 + x) = 6(x + -4)

Multiply (-4 + x) * (8 + x)
(-4(8 + x) + x(8 + x)) = 6(x + -4)
((8 * -4 + x * -4) + x(8 + x)) = 6(x + -4)
((-32 + -4x) + x(8 + x)) = 6(x + -4)
(-32 + -4x + (8 * x + x * x)) = 6(x + -4)
(-32 + -4x + (8x + x2)) = 6(x + -4)

Combine like terms: -4x + 8x = 4x
(-32 + 4x + x2) = 6(x + -4)

Reorder the terms:
-32 + 4x + x2 = 6(-4 + x)
-32 + 4x + x2 = (-4 * 6 + x * 6)
-32 + 4x + x2 = (-24 + 6x)

Solving
-32 + 4x + x2 = -24 + 6x

Solving for variable 'x'.

Reorder the terms:
-32 + 24 + 4x + -6x + x2 = -24 + 6x + 24 + -6x

Combine like terms: -32 + 24 = -8
-8 + 4x + -6x + x2 = -24 + 6x + 24 + -6x

Combine like terms: 4x + -6x = -2x
-8 + -2x + x2 = -24 + 6x + 24 + -6x

Reorder the terms:
-8 + -2x + x2 = -24 + 24 + 6x + -6x

Combine like terms: -24 + 24 = 0
-8 + -2x + x2 = 0 + 6x + -6x
-8 + -2x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-8 + -2x + x2 = 0

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
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
Solution
x = {-2, 4}