8(x-2)-8(x-6)=(x-6)(x-2)

Solution for 8(x-2)-8(x-6)=(x-6)(x-2) equation:

Simplifying
8(x + -2) + -8(x + -6) = (x + -6)(x + -2)

Reorder the terms:
8(-2 + x) + -8(x + -6) = (x + -6)(x + -2)
(-2 * 8 + x * 8) + -8(x + -6) = (x + -6)(x + -2)
(-16 + 8x) + -8(x + -6) = (x + -6)(x + -2)

Reorder the terms:
-16 + 8x + -8(-6 + x) = (x + -6)(x + -2)
-16 + 8x + (-6 * -8 + x * -8) = (x + -6)(x + -2)
-16 + 8x + (48 + -8x) = (x + -6)(x + -2)

Reorder the terms:
-16 + 48 + 8x + -8x = (x + -6)(x + -2)

Combine like terms: -16 + 48 = 32
32 + 8x + -8x = (x + -6)(x + -2)

Combine like terms: 8x + -8x = 0
32 + 0 = (x + -6)(x + -2)
32 = (x + -6)(x + -2)

Reorder the terms:
32 = (-6 + x)(x + -2)

Reorder the terms:
32 = (-6 + x)(-2 + x)

Multiply (-6 + x) * (-2 + x)
32 = (-6(-2 + x) + x(-2 + x))
32 = ((-2 * -6 + x * -6) + x(-2 + x))
32 = ((12 + -6x) + x(-2 + x))
32 = (12 + -6x + (-2 * x + x * x))
32 = (12 + -6x + (-2x + x2))

Combine like terms: -6x + -2x = -8x
32 = (12 + -8x + x2)

Solving
32 = 12 + -8x + x2

Solving for variable 'x'.

Combine like terms: 32 + -12 = 20
20 + 8x + -1x2 = 12 + -8x + x2 + -12 + 8x + -1x2

Reorder the terms:
20 + 8x + -1x2 = 12 + -12 + -8x + 8x + x2 + -1x2

Combine like terms: 12 + -12 = 0
20 + 8x + -1x2 = 0 + -8x + 8x + x2 + -1x2
20 + 8x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
20 + 8x + -1x2 = 0 + x2 + -1x2
20 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 8x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(2 + x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {10, -2}