2u^2+2u-24=0

Solution for 2u^2+2u-24=0 equation:

Simplifying
2u2 + 2u + -24 = 0

Reorder the terms:
-24 + 2u + 2u2 = 0

Solving
-24 + 2u + 2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + u + u2) = 0

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

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

Simplifying
-4 + -1u = 0

Solving
-4 + -1u = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1u = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1u = 0 + 4
-1u = 0 + 4

Combine like terms: 0 + 4 = 4
-1u = 4

Divide each side by '-1'.
u = -4

Simplifying
u = -4
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 = {-4, 3}