24n^2+2n-12=0

Solution for 24n^2+2n-12=0 equation:

Simplifying
24n2 + 2n + -12 = 0

Reorder the terms:
-12 + 2n + 24n2 = 0

Solving
-12 + 2n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + n + 12n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4n)' equal to zero and attempt to solve:

Simplifying
-3 + -4n = 0

Solving
-3 + -4n = 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 + -4n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4n = 0 + 3
-4n = 0 + 3

Combine like terms: 0 + 3 = 3
-4n = 3

Divide each side by '-4'.
n = -0.75

Simplifying
n = -0.75
Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-0.75, 0.6666666667}