(x-1)(x-12)=0

Solution for (x-1)(x-12)=0 equation:

Simplifying
(x + -1)(x + -12) = 0

Reorder the terms:
(-1 + x)(x + -12) = 0

Reorder the terms:
(-1 + x)(-12 + x) = 0

Multiply (-1 + x) * (-12 + x)
(-1(-12 + x) + x(-12 + x)) = 0
((-12 * -1 + x * -1) + x(-12 + x)) = 0
((12 + -1x) + x(-12 + x)) = 0
(12 + -1x + (-12 * x + x * x)) = 0
(12 + -1x + (-12x + x2)) = 0

Combine like terms: -1x + -12x = -13x
(12 + -13x + x2) = 0

Solving
12 + -13x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 12}