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 + -1n)) = 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 + -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 = {-3.5, 3}