3n^2=6n+144

Solution for 3n^2=6n+144 equation:

Simplifying
3n2 = 6n + 144

Reorder the terms:
3n2 = 144 + 6n

Solving
3n2 = 144 + 6n

Solving for variable 'n'.

Reorder the terms:
-144 + -6n + 3n2 = 144 + 6n + -144 + -6n

Reorder the terms:
-144 + -6n + 3n2 = 144 + -144 + 6n + -6n

Combine like terms: 144 + -144 = 0
-144 + -6n + 3n2 = 0 + 6n + -6n
-144 + -6n + 3n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-144 + -6n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-48 + -2n + n2) = 0

Factor a trinomial.
3((-6 + -1n)(8 + -1n)) = 0

Ignore the factor 3.
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}