-4n^2+2n+90=0

Solution for -4n^2+2n+90=0 equation:

Simplifying
-4n2 + 2n + 90 = 0

Reorder the terms:
90 + 2n + -4n2 = 0

Solving
90 + 2n + -4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45 + n + -2n2) = 0

Factor a trinomial.
2((5 + -1n)(9 + 2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Subproblem 2
Set the factor '(9 + 2n)' equal to zero and attempt to solve:

Simplifying
9 + 2n = 0

Solving
9 + 2n = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2n = 0 + -9
2n = 0 + -9

Combine like terms: 0 + -9 = -9
2n = -9

Divide each side by '2'.
n = -4.5

Simplifying
n = -4.5
Solution
n = {5, -4.5}