3n^2-15=12n

Solution for 3n^2-15=12n equation:

Simplifying
3n2 + -15 = 12n

Reorder the terms:
-15 + 3n2 = 12n

Solving
-15 + 3n2 = 12n

Solving for variable 'n'.

Reorder the terms:
-15 + -12n + 3n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
-15 + -12n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4n + n2) = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
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 = {-1, 5}