(x-12)(x-10)=0

Solution for (x-12)(x-10)=0 equation:

Simplifying
(x + -12)(x + -10) = 0

Reorder the terms:
(-12 + x)(x + -10) = 0

Reorder the terms:
(-12 + x)(-10 + x) = 0

Multiply (-12 + x) * (-10 + x)
(-12(-10 + x) + x(-10 + x)) = 0
((-10 * -12 + x * -12) + x(-10 + x)) = 0
((120 + -12x) + x(-10 + x)) = 0
(120 + -12x + (-10 * x + x * x)) = 0
(120 + -12x + (-10x + x2)) = 0

Combine like terms: -12x + -10x = -22x
(120 + -22x + x2) = 0

Solving
120 + -22x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(10 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
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 = {10, 12}