2n^2=132+10n

Solution for 2n^2=132+10n equation:

Simplifying
2n2 = 132 + 10n

Solving
2n2 = 132 + 10n

Solving for variable 'n'.

Reorder the terms:
-132 + -10n + 2n2 = 132 + 10n + -132 + -10n

Reorder the terms:
-132 + -10n + 2n2 = 132 + -132 + 10n + -10n

Combine like terms: 132 + -132 = 0
-132 + -10n + 2n2 = 0 + 10n + -10n
-132 + -10n + 2n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-132 + -10n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-66 + -5n + n2) = 0

Factor a trinomial.
2((-6 + -1n)(11 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

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

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

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

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

Simplifying
n = -6
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 = {-6, 11}