(x-5)(x-6)=12

Solution for (x-5)(x-6)=12 equation:

Simplifying
(x + -5)(x + -6) = 12

Reorder the terms:
(-5 + x)(x + -6) = 12

Reorder the terms:
(-5 + x)(-6 + x) = 12

Multiply (-5 + x) * (-6 + x)
(-5(-6 + x) + x(-6 + x)) = 12
((-6 * -5 + x * -5) + x(-6 + x)) = 12
((30 + -5x) + x(-6 + x)) = 12
(30 + -5x + (-6 * x + x * x)) = 12
(30 + -5x + (-6x + x2)) = 12

Combine like terms: -5x + -6x = -11x
(30 + -11x + x2) = 12

Solving
30 + -11x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
30 + -12 + -11x + x2 = 12 + -12

Combine like terms: 30 + -12 = 18
18 + -11x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
18 + -11x + x2 = 0

Factor a trinomial.
(2 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {2, 9}