(x-22)(x+12)=0

Solution for (x-22)(x+12)=0 equation:

Simplifying
(x + -22)(x + 12) = 0

Reorder the terms:
(-22 + x)(x + 12) = 0

Reorder the terms:
(-22 + x)(12 + x) = 0

Multiply (-22 + x) * (12 + x)
(-22(12 + x) + x(12 + x)) = 0
((12 * -22 + x * -22) + x(12 + x)) = 0
((-264 + -22x) + x(12 + x)) = 0
(-264 + -22x + (12 * x + x * x)) = 0
(-264 + -22x + (12x + x2)) = 0

Combine like terms: -22x + 12x = -10x
(-264 + -10x + x2) = 0

Solving
-264 + -10x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-12 + -1x)(22 + -1x) = 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 '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-12, 22}