6u^2=-9u

Solution for 6u^2=-9u equation:

Simplifying
6u2 = -9u

Solving
6u2 = -9u

Solving for variable 'u'.

Reorder the terms:
9u + 6u2 = -9u + 9u

Combine like terms: -9u + 9u = 0
9u + 6u2 = 0

Factor out the Greatest Common Factor (GCF), '3u'.
3u(3 + 2u) = 0

Ignore the factor 3.
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 '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 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 + 2u = 0 + -3

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

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

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {0, -1.5}