20n^2-48n-36=0

Solution for 20n^2-48n-36=0 equation:

Simplifying
20n2 + -48n + -36 = 0

Reorder the terms:
-36 + -48n + 20n2 = 0

Solving
-36 + -48n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + -12n + 5n2) = 0

Factor a trinomial.
4((-3 + -5n)(3 + -1n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve:

Simplifying
-3 + -5n = 0

Solving
-3 + -5n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5n = 0 + 3
-5n = 0 + 3

Combine like terms: 0 + 3 = 3
-5n = 3

Divide each side by '-5'.
n = -0.6

Simplifying
n = -0.6
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.6, 3}