4n^2-9n-90=0

Solution for 4n^2-9n-90=0 equation:

Simplifying
4n2 + -9n + -90 = 0

Reorder the terms:
-90 + -9n + 4n2 = 0

Solving
-90 + -9n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-15 + -4n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -4n)' equal to zero and attempt to solve:

Simplifying
-15 + -4n = 0

Solving
-15 + -4n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4n = 0 + 15
-4n = 0 + 15

Combine like terms: 0 + 15 = 15
-4n = 15

Divide each side by '-4'.
n = -3.75

Simplifying
n = -3.75
Subproblem 2
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
Solution
n = {-3.75, 6}