(x-2)(x-2)=2x^2+5x+18

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Solution for (x-2)(x-2)=2x^2+5x+18 equation: 


Simplifying
(x + -2)(x + -2) = 2x2 + 5x + 18

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

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

Multiply (-2 + x) * (-2 + x)
(-2(-2 + x) + x(-2 + x)) = 2x2 + 5x + 18
((-2 * -2 + x * -2) + x(-2 + x)) = 2x2 + 5x + 18
((4 + -2x) + x(-2 + x)) = 2x2 + 5x + 18
(4 + -2x + (-2 * x + x * x)) = 2x2 + 5x + 18
(4 + -2x + (-2x + x2)) = 2x2 + 5x + 18

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

Reorder the terms:
4 + -4x + x2 = 18 + 5x + 2x2

Solving
4 + -4x + x2 = 18 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
4 + -18 + -4x + -5x + x2 + -2x2 = 18 + 5x + 2x2 + -18 + -5x + -2x2

Combine like terms: 4 + -18 = -14
-14 + -4x + -5x + x2 + -2x2 = 18 + 5x + 2x2 + -18 + -5x + -2x2

Combine like terms: -4x + -5x = -9x
-14 + -9x + x2 + -2x2 = 18 + 5x + 2x2 + -18 + -5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-14 + -9x + -1x2 = 18 + 5x + 2x2 + -18 + -5x + -2x2

Reorder the terms:
-14 + -9x + -1x2 = 18 + -18 + 5x + -5x + 2x2 + -2x2

Combine like terms: 18 + -18 = 0
-14 + -9x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2
-14 + -9x + -1x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-14 + -9x + -1x2 = 0 + 2x2 + -2x2
-14 + -9x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-14 + -9x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 9x + x2) = 0

Factor a trinomial.
-1((7 + x)(2 + x)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

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 = {-7, -2}

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