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

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

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

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

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

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

Combine like terms: -6x + 5x = -1x
(-30 + -1x + x2) = 12

Solving
-30 + -1x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
-30 + -12 + -1x + x2 = 12 + -12

Combine like terms: -30 + -12 = -42
-42 + -1x + x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-42 + -1x + x2 = 0

Factor a trinomial.
(-6 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 7}