2n^2-32n=-56

Solution for 2n^2-32n=-56 equation:

Simplifying
2n2 + -32n = -56

Reorder the terms:
-32n + 2n2 = -56

Solving
-32n + 2n2 = -56

Solving for variable 'n'.

Reorder the terms:
56 + -32n + 2n2 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + -32n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -16n + n2) = 0

Factor a trinomial.
2((2 + -1n)(14 + -1n)) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {2, 14}