(x-2)(2x+1)-9=9(1-x)

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Solution for (x-2)(2x+1)-9=9(1-x) equation: 


Simplifying
(x + -2)(2x + 1) + -9 = 9(1 + -1x)

Reorder the terms:
(-2 + x)(2x + 1) + -9 = 9(1 + -1x)

Reorder the terms:
(-2 + x)(1 + 2x) + -9 = 9(1 + -1x)

Multiply (-2 + x) * (1 + 2x)
(-2(1 + 2x) + x(1 + 2x)) + -9 = 9(1 + -1x)
((1 * -2 + 2x * -2) + x(1 + 2x)) + -9 = 9(1 + -1x)
((-2 + -4x) + x(1 + 2x)) + -9 = 9(1 + -1x)
(-2 + -4x + (1 * x + 2x * x)) + -9 = 9(1 + -1x)
(-2 + -4x + (1x + 2x2)) + -9 = 9(1 + -1x)

Combine like terms: -4x + 1x = -3x
(-2 + -3x + 2x2) + -9 = 9(1 + -1x)

Reorder the terms:
-2 + -9 + -3x + 2x2 = 9(1 + -1x)

Combine like terms: -2 + -9 = -11
-11 + -3x + 2x2 = 9(1 + -1x)
-11 + -3x + 2x2 = (1 * 9 + -1x * 9)
-11 + -3x + 2x2 = (9 + -9x)

Solving
-11 + -3x + 2x2 = 9 + -9x

Solving for variable 'x'.

Reorder the terms:
-11 + -9 + -3x + 9x + 2x2 = 9 + -9x + -9 + 9x

Combine like terms: -11 + -9 = -20
-20 + -3x + 9x + 2x2 = 9 + -9x + -9 + 9x

Combine like terms: -3x + 9x = 6x
-20 + 6x + 2x2 = 9 + -9x + -9 + 9x

Reorder the terms:
-20 + 6x + 2x2 = 9 + -9 + -9x + 9x

Combine like terms: 9 + -9 = 0
-20 + 6x + 2x2 = 0 + -9x + 9x
-20 + 6x + 2x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-20 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 3x + x2) = 0

Factor a trinomial.
2((-5 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -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 = {-5, 2}

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