6u^2+u=0

Solution for 6u^2+u=0 equation:

Simplifying
6u2 + u = 0

Reorder the terms:
u + 6u2 = 0

Solving
u + 6u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(1 + 6u) = 0

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 '(1 + 6u)' equal to zero and attempt to solve:

Simplifying
1 + 6u = 0

Solving
1 + 6u = 0

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

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

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

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

Divide each side by '6'.
u = -0.1666666667

Simplifying
u = -0.1666666667
Solution
u = {0, -0.1666666667}