6n^2=288+12n

Solution for 6n^2=288+12n equation:

Simplifying
6n2 = 288 + 12n

Solving
6n2 = 288 + 12n

Solving for variable 'n'.

Reorder the terms:
-288 + -12n + 6n2 = 288 + 12n + -288 + -12n

Reorder the terms:
-288 + -12n + 6n2 = 288 + -288 + 12n + -12n

Combine like terms: 288 + -288 = 0
-288 + -12n + 6n2 = 0 + 12n + -12n
-288 + -12n + 6n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
-288 + -12n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-48 + -2n + n2) = 0

Factor a trinomial.
6((-6 + -1n)(8 + -1n)) = 0

Ignore the factor 6.
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 '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-6, 8}