4n^2=108+6n

Solution for 4n^2=108+6n equation:

Simplifying
4n2 = 108 + 6n

Solving
4n2 = 108 + 6n

Solving for variable 'n'.

Reorder the terms:
-108 + -6n + 4n2 = 108 + 6n + -108 + -6n

Reorder the terms:
-108 + -6n + 4n2 = 108 + -108 + 6n + -6n

Combine like terms: 108 + -108 = 0
-108 + -6n + 4n2 = 0 + 6n + -6n
-108 + -6n + 4n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-108 + -6n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + -3n + 2n2) = 0

Factor a trinomial.
2((-9 + -2n)(6 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -2n)' equal to zero and attempt to solve:

Simplifying
-9 + -2n = 0

Solving
-9 + -2n = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2n = 0 + 9
-2n = 0 + 9

Combine like terms: 0 + 9 = 9
-2n = 9

Divide each side by '-2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
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
Solution
n = {-4.5, 6}