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

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


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

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

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

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

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

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

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

Multiply (9 + 2x) * (-2 + x)
-2 + -1x + x2 = (9(-2 + x) + 2x * (-2 + x))
-2 + -1x + x2 = ((-2 * 9 + x * 9) + 2x * (-2 + x))
-2 + -1x + x2 = ((-18 + 9x) + 2x * (-2 + x))
-2 + -1x + x2 = (-18 + 9x + (-2 * 2x + x * 2x))
-2 + -1x + x2 = (-18 + 9x + (-4x + 2x2))

Combine like terms: 9x + -4x = 5x
-2 + -1x + x2 = (-18 + 5x + 2x2)

Solving
-2 + -1x + x2 = -18 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 18 + -1x + -5x + x2 + -2x2 = -18 + 5x + 2x2 + 18 + -5x + -2x2

Combine like terms: -2 + 18 = 16
16 + -1x + -5x + x2 + -2x2 = -18 + 5x + 2x2 + 18 + -5x + -2x2

Combine like terms: -1x + -5x = -6x
16 + -6x + x2 + -2x2 = -18 + 5x + 2x2 + 18 + -5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
16 + -6x + -1x2 = -18 + 5x + 2x2 + 18 + -5x + -2x2

Reorder the terms:
16 + -6x + -1x2 = -18 + 18 + 5x + -5x + 2x2 + -2x2

Combine like terms: -18 + 18 = 0
16 + -6x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2
16 + -6x + -1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
16 + -6x + -1x2 = 0 + 2x2 + -2x2
16 + -6x + -1x2 = 2x2 + -2x2

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

Factor a trinomial.
(2 + -1x)(8 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {2, -8}

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