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

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

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

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

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

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

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

Solving
-12 + 4x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-12 + -180 + 4x + x2 = 180 + -180

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

Combine like terms: 180 + -180 = 0
-192 + 4x + x2 = 0

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

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 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 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
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
Solution
x = {-16, 12}