3n^2-54=-9n

Solution for 3n^2-54=-9n equation:

Simplifying
3n2 + -54 = -9n

Reorder the terms:
-54 + 3n2 = -9n

Solving
-54 + 3n2 = -9n

Solving for variable 'n'.

Reorder the terms:
-54 + 9n + 3n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
-54 + 9n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + 3n + n2) = 0

Factor a trinomial.
3((-6 + -1n)(3 + -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 '(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
Solution
n = {-6, 3}