(x-2)(x+12)=8x

Solution for (x-2)(x+12)=8x equation:

Simplifying
(x + -2)(x + 12) = 8x

Reorder the terms:
(-2 + x)(x + 12) = 8x

Reorder the terms:
(-2 + x)(12 + x) = 8x

Multiply (-2 + x) * (12 + x)
(-2(12 + x) + x(12 + x)) = 8x
((12 * -2 + x * -2) + x(12 + x)) = 8x
((-24 + -2x) + x(12 + x)) = 8x
(-24 + -2x + (12 * x + x * x)) = 8x
(-24 + -2x + (12x + x2)) = 8x

Combine like terms: -2x + 12x = 10x
(-24 + 10x + x2) = 8x

Solving
-24 + 10x + x2 = 8x

Solving for variable 'x'.

Reorder the terms:
-24 + 10x + -8x + x2 = 8x + -8x

Combine like terms: 10x + -8x = 2x
-24 + 2x + x2 = 8x + -8x

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

Factor a trinomial.
(-6 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 4}