(x-1)(x-5)=12

Solution for (x-1)(x-5)=12 equation:

Simplifying
(x + -1)(x + -5) = 12

Reorder the terms:
(-1 + x)(x + -5) = 12

Reorder the terms:
(-1 + x)(-5 + x) = 12

Multiply (-1 + x) * (-5 + x)
(-1(-5 + x) + x(-5 + x)) = 12
((-5 * -1 + x * -1) + x(-5 + x)) = 12
((5 + -1x) + x(-5 + x)) = 12
(5 + -1x + (-5 * x + x * x)) = 12
(5 + -1x + (-5x + x2)) = 12

Combine like terms: -1x + -5x = -6x
(5 + -6x + x2) = 12

Solving
5 + -6x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
5 + -12 + -6x + x2 = 12 + -12

Combine like terms: 5 + -12 = -7
-7 + -6x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-7 + -6x + x2 = 0

Factor a trinomial.
(-1 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-1, 7}