9u^2-3u-6=0

Solution for 9u^2-3u-6=0 equation:

Simplifying
9u2 + -3u + -6 = 0

Reorder the terms:
-6 + -3u + 9u2 = 0

Solving
-6 + -3u + 9u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1u + 3u2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -3u)' equal to zero and attempt to solve:

Simplifying
-2 + -3u = 0

Solving
-2 + -3u = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3u = 0 + 2

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

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

Divide each side by '-3'.
u = -0.6666666667

Simplifying
u = -0.6666666667
Subproblem 2
Set the factor '(1 + -1u)' equal to zero and attempt to solve:

Simplifying
1 + -1u = 0

Solving
1 + -1u = 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 + -1u = 0 + -1

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

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

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

Simplifying
u = 1
Solution
u = {-0.6666666667, 1}