2n^2-80=-12n

Solution for 2n^2-80=-12n equation:

Simplifying
2n2 + -80 = -12n

Reorder the terms:
-80 + 2n2 = -12n

Solving
-80 + 2n2 = -12n

Solving for variable 'n'.

Reorder the terms:
-80 + 12n + 2n2 = -12n + 12n

Combine like terms: -12n + 12n = 0
-80 + 12n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + 6n + n2) = 0

Factor a trinomial.
2((-10 + -1n)(4 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-10, 4}