(x-2)(x+1)+(x-2)(x+8)=0

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Solution for (x-2)(x+1)+(x-2)(x+8)=0 equation: 


Simplifying
(x + -2)(x + 1) + (x + -2)(x + 8) = 0

Reorder the terms:
(-2 + x)(x + 1) + (x + -2)(x + 8) = 0

Reorder the terms:
(-2 + x)(1 + x) + (x + -2)(x + 8) = 0

Multiply (-2 + x) * (1 + x)
(-2(1 + x) + x(1 + x)) + (x + -2)(x + 8) = 0
((1 * -2 + x * -2) + x(1 + x)) + (x + -2)(x + 8) = 0
((-2 + -2x) + x(1 + x)) + (x + -2)(x + 8) = 0
(-2 + -2x + (1 * x + x * x)) + (x + -2)(x + 8) = 0
(-2 + -2x + (1x + x2)) + (x + -2)(x + 8) = 0

Combine like terms: -2x + 1x = -1x
(-2 + -1x + x2) + (x + -2)(x + 8) = 0

Reorder the terms:
-2 + -1x + x2 + (-2 + x)(x + 8) = 0

Reorder the terms:
-2 + -1x + x2 + (-2 + x)(8 + x) = 0

Multiply (-2 + x) * (8 + x)
-2 + -1x + x2 + (-2(8 + x) + x(8 + x)) = 0
-2 + -1x + x2 + ((8 * -2 + x * -2) + x(8 + x)) = 0
-2 + -1x + x2 + ((-16 + -2x) + x(8 + x)) = 0
-2 + -1x + x2 + (-16 + -2x + (8 * x + x * x)) = 0
-2 + -1x + x2 + (-16 + -2x + (8x + x2)) = 0

Combine like terms: -2x + 8x = 6x
-2 + -1x + x2 + (-16 + 6x + x2) = 0

Reorder the terms:
-2 + -16 + -1x + 6x + x2 + x2 = 0

Combine like terms: -2 + -16 = -18
-18 + -1x + 6x + x2 + x2 = 0

Combine like terms: -1x + 6x = 5x
-18 + 5x + x2 + x2 = 0

Combine like terms: x2 + x2 = 2x2
-18 + 5x + 2x2 = 0

Solving
-18 + 5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -2x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 2
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
Solution
x = {-4.5, 2}

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