180=(x-2)(x+6)

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Solution for 180=(x-2)(x+6) equation: 


Simplifying
180 = (x + -2)(x + 6)

Reorder the terms:
180 = (-2 + x)(x + 6)

Reorder the terms:
180 = (-2 + x)(6 + x)

Multiply (-2 + x) * (6 + x)
180 = (-2(6 + x) + x(6 + x))
180 = ((6 * -2 + x * -2) + x(6 + x))
180 = ((-12 + -2x) + x(6 + x))
180 = (-12 + -2x + (6 * x + x * x))
180 = (-12 + -2x + (6x + x2))

Combine like terms: -2x + 6x = 4x
180 = (-12 + 4x + x2)

Solving
180 = -12 + 4x + x2

Solving for variable 'x'.

Combine like terms: 180 + 12 = 192
192 + -4x + -1x2 = -12 + 4x + x2 + 12 + -4x + -1x2

Reorder the terms:
192 + -4x + -1x2 = -12 + 12 + 4x + -4x + x2 + -1x2

Combine like terms: -12 + 12 = 0
192 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
192 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
192 + -4x + -1x2 = 0 + x2 + -1x2
192 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
192 + -4x + -1x2 = 0

Factor a trinomial.
(12 + -1x)(16 + x) = 0


Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12

Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {12, -16}

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