-6n^2+63=-3n

Solution for -6n^2+63=-3n equation:

Simplifying
-6n2 + 63 = -3n

Reorder the terms:
63 + -6n2 = -3n

Solving
63 + -6n2 = -3n

Solving for variable 'n'.

Reorder the terms:
63 + 3n + -6n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
63 + 3n + -6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + n + -2n2) = 0

Factor a trinomial.
3((7 + -2n)(3 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + -2n)' equal to zero and attempt to solve:

Simplifying
7 + -2n = 0

Solving
7 + -2n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 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 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Solution
n = {3.5, -3}