(x-2)(x+8)=8(x+1)

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Solution for (x-2)(x+8)=8(x+1) equation: 


Simplifying
(x + -2)(x + 8) = 8(x + 1)

Reorder the terms:
(-2 + x)(x + 8) = 8(x + 1)

Reorder the terms:
(-2 + x)(8 + x) = 8(x + 1)

Multiply (-2 + x) * (8 + x)
(-2(8 + x) + x(8 + x)) = 8(x + 1)
((8 * -2 + x * -2) + x(8 + x)) = 8(x + 1)
((-16 + -2x) + x(8 + x)) = 8(x + 1)
(-16 + -2x + (8 * x + x * x)) = 8(x + 1)
(-16 + -2x + (8x + x2)) = 8(x + 1)

Combine like terms: -2x + 8x = 6x
(-16 + 6x + x2) = 8(x + 1)

Reorder the terms:
-16 + 6x + x2 = 8(1 + x)
-16 + 6x + x2 = (1 * 8 + x * 8)
-16 + 6x + x2 = (8 + 8x)

Solving
-16 + 6x + x2 = 8 + 8x

Solving for variable 'x'.

Reorder the terms:
-16 + -8 + 6x + -8x + x2 = 8 + 8x + -8 + -8x

Combine like terms: -16 + -8 = -24
-24 + 6x + -8x + x2 = 8 + 8x + -8 + -8x

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

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

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

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

Factor a trinomial.
(-4 + -1x)(6 + -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 '(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
Solution
x = {-4, 6}

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