6n^2=12n+90

Solution for 6n^2=12n+90 equation:

Simplifying
6n2 = 12n + 90

Reorder the terms:
6n2 = 90 + 12n

Solving
6n2 = 90 + 12n

Solving for variable 'n'.

Reorder the terms:
-90 + -12n + 6n2 = 90 + 12n + -90 + -12n

Reorder the terms:
-90 + -12n + 6n2 = 90 + -90 + 12n + -12n

Combine like terms: 90 + -90 = 0
-90 + -12n + 6n2 = 0 + 12n + -12n
-90 + -12n + 6n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
-90 + -12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-15 + -2n + n2) = 0

Factor a trinomial.
6((-3 + -1n)(5 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-3, 5}