(x-1)(x-2)=12

Solution for (x-1)(x-2)=12 equation:

Simplifying
(x + -1)(x + -2) = 12

Reorder the terms:
(-1 + x)(x + -2) = 12

Reorder the terms:
(-1 + x)(-2 + x) = 12

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = 12
((-2 * -1 + x * -1) + x(-2 + x)) = 12
((2 + -1x) + x(-2 + x)) = 12
(2 + -1x + (-2 * x + x * x)) = 12
(2 + -1x + (-2x + x2)) = 12

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = 12

Solving
2 + -3x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
2 + -12 + -3x + x2 = 12 + -12

Combine like terms: 2 + -12 = -10
-10 + -3x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-10 + -3x + x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}