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

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

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

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

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

Multiply (3 + n) * (-2 + n)
(3(-2 + n) + n(-2 + n)) + -126 = 0
((-2 * 3 + n * 3) + n(-2 + n)) + -126 = 0
((-6 + 3n) + n(-2 + n)) + -126 = 0
(-6 + 3n + (-2 * n + n * n)) + -126 = 0
(-6 + 3n + (-2n + n2)) + -126 = 0

Combine like terms: 3n + -2n = 1n
(-6 + 1n + n2) + -126 = 0

Reorder the terms:
-6 + -126 + 1n + n2 = 0

Combine like terms: -6 + -126 = -132
-132 + 1n + n2 = 0

Solving
-132 + 1n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1n = 0 + 12
-1n = 0 + 12

Combine like terms: 0 + 12 = 12
-1n = 12

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

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

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

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

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

Simplifying
n = 11
Solution
n = {-12, 11}