12u^2-28u-24=0

Solution for 12u^2-28u-24=0 equation:

Simplifying
12u2 + -28u + -24 = 0

Reorder the terms:
-24 + -28u + 12u2 = 0

Solving
-24 + -28u + 12u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-6 + -7u + 3u2) = 0

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

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

Simplifying
-2 + -3u = 0

Solving
-2 + -3u = 0

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

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

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

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

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

Simplifying
u = -0.6666666667
Subproblem 2
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

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

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

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

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

Simplifying
u = 3
Solution
u = {-0.6666666667, 3}