(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 = -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}