24n^2-18n-15=0

Solution for 24n^2-18n-15=0 equation:

Simplifying
24n2 + -18n + -15 = 0

Reorder the terms:
-15 + -18n + 24n2 = 0

Solving
-15 + -18n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -6n + 8n2) = 0

Factor a trinomial.
3((-1 + -2n)(5 + -4n)) = 0

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2n = 0 + 1
-2n = 0 + 1

Combine like terms: 0 + 1 = 1
-2n = 1

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(5 + -4n)' equal to zero and attempt to solve:

Simplifying
5 + -4n = 0

Solving
5 + -4n = 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 + -4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4n = 0 + -5
-4n = 0 + -5

Combine like terms: 0 + -5 = -5
-4n = -5

Divide each side by '-4'.
n = 1.25

Simplifying
n = 1.25
Solution
n = {-0.5, 1.25}