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 + -1n + 2n2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-4.5, 5}