(x+2)(x-3)-126=0

Solution for (x+2)(x-3)-126=0 equation:

Simplifying
(x + 2)(x + -3) + -126 = 0

Reorder the terms:
(2 + x)(x + -3) + -126 = 0

Reorder the terms:
(2 + x)(-3 + x) + -126 = 0

Multiply (2 + x) * (-3 + x)
(2(-3 + x) + x(-3 + x)) + -126 = 0
((-3 * 2 + x * 2) + x(-3 + x)) + -126 = 0
((-6 + 2x) + x(-3 + x)) + -126 = 0
(-6 + 2x + (-3 * x + x * x)) + -126 = 0
(-6 + 2x + (-3x + x2)) + -126 = 0

Combine like terms: 2x + -3x = -1x
(-6 + -1x + x2) + -126 = 0

Reorder the terms:
-6 + -126 + -1x + x2 = 0

Combine like terms: -6 + -126 = -132
-132 + -1x + x2 = 0

Solving
-132 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-11 + -1x)(12 + -1x) = 0

Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
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 = {-11, 12}