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

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

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

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

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

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

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

Solving
-6 + 1x + x2 = 126

Solving for variable 'x'.

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-12, 11}