6u^2+24u-126=0

Solution for 6u^2+24u-126=0 equation:

Simplifying
6u2 + 24u + -126 = 0

Reorder the terms:
-126 + 24u + 6u2 = 0

Solving
-126 + 24u + 6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + 4u + u2) = 0

Factor a trinomial.
6((-7 + -1u)(3 + -1u)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -1u)' equal to zero and attempt to solve:

Simplifying
-7 + -1u = 0

Solving
-7 + -1u = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1u = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1u = 0 + 7
-1u = 0 + 7

Combine like terms: 0 + 7 = 7
-1u = 7

Divide each side by '-1'.
u = -7

Simplifying
u = -7
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 = {-7, 3}