12u^3+58u^2-84u=0

Solution for 12u^3+58u^2-84u=0 equation:

Simplifying
12u3 + 58u2 + -84u = 0

Reorder the terms:
-84u + 58u2 + 12u3 = 0

Solving
-84u + 58u2 + 12u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2u'.
2u(-42 + 29u + 6u2) = 0

Factor a trinomial.
2u((-6 + -1u)(7 + -6u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

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

Simplifying
u = 0
Subproblem 2
Set the factor '(-6 + -1u)' equal to zero and attempt to solve:

Simplifying
-6 + -1u = 0

Solving
-6 + -1u = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1u = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1u = 0 + 6
-1u = 0 + 6

Combine like terms: 0 + 6 = 6
-1u = 6

Divide each side by '-1'.
u = -6

Simplifying
u = -6
Subproblem 3
Set the factor '(7 + -6u)' equal to zero and attempt to solve:

Simplifying
7 + -6u = 0

Solving
7 + -6u = 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 + -6u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6u = 0 + -7
-6u = 0 + -7

Combine like terms: 0 + -7 = -7
-6u = -7

Divide each side by '-6'.
u = 1.166666667

Simplifying
u = 1.166666667
Solution
u = {0, -6, 1.166666667}