2n^2=8n+120

Solution for 2n^2=8n+120 equation:

Simplifying
2n2 = 8n + 120

Reorder the terms:
2n2 = 120 + 8n

Solving
2n2 = 120 + 8n

Solving for variable 'n'.

Reorder the terms:
-120 + -8n + 2n2 = 120 + 8n + -120 + -8n

Reorder the terms:
-120 + -8n + 2n2 = 120 + -120 + 8n + -8n

Combine like terms: 120 + -120 = 0
-120 + -8n + 2n2 = 0 + 8n + -8n
-120 + -8n + 2n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-120 + -8n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + -4n + n2) = 0

Factor a trinomial.
2((-6 + -1n)(10 + -1n)) = 0

Ignore the factor 2.
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 '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-6, 10}