6n^2=-2n+48

Solution for 6n^2=-2n+48 equation:

Simplifying
6n2 = -2n + 48

Reorder the terms:
6n2 = 48 + -2n

Solving
6n2 = 48 + -2n

Solving for variable 'n'.

Reorder the terms:
-48 + 2n + 6n2 = 48 + -2n + -48 + 2n

Reorder the terms:
-48 + 2n + 6n2 = 48 + -48 + -2n + 2n

Combine like terms: 48 + -48 = 0
-48 + 2n + 6n2 = 0 + -2n + 2n
-48 + 2n + 6n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-48 + 2n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + n + 3n2) = 0

Factor a trinomial.
2((-3 + -1n)(8 + -3n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(8 + -3n)' equal to zero and attempt to solve:

Simplifying
8 + -3n = 0

Solving
8 + -3n = 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 + -3n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3n = 0 + -8
-3n = 0 + -8

Combine like terms: 0 + -8 = -8
-3n = -8

Divide each side by '-3'.
n = 2.666666667

Simplifying
n = 2.666666667
Solution
n = {-3, 2.666666667}