(x)(x+5)+162=2(x+5)(x-2)

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Solution for (x)(x+5)+162=2(x+5)(x-2) equation: 


Simplifying
(x)(x + 5) + 162 = 2(x + 5)(x + -2)

Reorder the terms:
x(5 + x) + 162 = 2(x + 5)(x + -2)
(5 * x + x * x) + 162 = 2(x + 5)(x + -2)
(5x + x2) + 162 = 2(x + 5)(x + -2)

Reorder the terms:
162 + 5x + x2 = 2(x + 5)(x + -2)

Reorder the terms:
162 + 5x + x2 = 2(5 + x)(x + -2)

Reorder the terms:
162 + 5x + x2 = 2(5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
162 + 5x + x2 = 2(5(-2 + x) + x(-2 + x))
162 + 5x + x2 = 2((-2 * 5 + x * 5) + x(-2 + x))
162 + 5x + x2 = 2((-10 + 5x) + x(-2 + x))
162 + 5x + x2 = 2(-10 + 5x + (-2 * x + x * x))
162 + 5x + x2 = 2(-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
162 + 5x + x2 = 2(-10 + 3x + x2)
162 + 5x + x2 = (-10 * 2 + 3x * 2 + x2 * 2)
162 + 5x + x2 = (-20 + 6x + 2x2)

Solving
162 + 5x + x2 = -20 + 6x + 2x2

Solving for variable 'x'.

Reorder the terms:
162 + 20 + 5x + -6x + x2 + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Combine like terms: 162 + 20 = 182
182 + 5x + -6x + x2 + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Combine like terms: 5x + -6x = -1x
182 + -1x + x2 + -2x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Combine like terms: x2 + -2x2 = -1x2
182 + -1x + -1x2 = -20 + 6x + 2x2 + 20 + -6x + -2x2

Reorder the terms:
182 + -1x + -1x2 = -20 + 20 + 6x + -6x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
182 + -1x + -1x2 = 0 + 6x + -6x + 2x2 + -2x2
182 + -1x + -1x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
182 + -1x + -1x2 = 0 + 2x2 + -2x2
182 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
182 + -1x + -1x2 = 0

Factor a trinomial.
(13 + -1x)(14 + x) = 0


Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {13, -14}

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