-2n^2+2n+53=-7

Solution for -2n^2+2n+53=-7 equation:

Simplifying
-2n2 + 2n + 53 = -7

Reorder the terms:
53 + 2n + -2n2 = -7

Solving
53 + 2n + -2n2 = -7

Solving for variable 'n'.

Reorder the terms:
53 + 7 + 2n + -2n2 = -7 + 7

Combine like terms: 53 + 7 = 60
60 + 2n + -2n2 = -7 + 7

Combine like terms: -7 + 7 = 0
60 + 2n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + n + -1n2) = 0

Factor a trinomial.
2((6 + -1n)(5 + n)) = 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 '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {6, -5}