24n^2+28n-132=0

Solution for 24n^2+28n-132=0 equation:

Simplifying
24n2 + 28n + -132 = 0

Reorder the terms:
-132 + 28n + 24n2 = 0

Solving
-132 + 28n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-33 + 7n + 6n2) = 0

Factor a trinomial.
4((-3 + -1n)(11 + -6n)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(11 + -6n)' equal to zero and attempt to solve:

Simplifying
11 + -6n = 0

Solving
11 + -6n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -6n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6n = 0 + -11
-6n = 0 + -11

Combine like terms: 0 + -11 = -11
-6n = -11

Divide each side by '-6'.
n = 1.833333333

Simplifying
n = 1.833333333
Solution
n = {-3, 1.833333333}