3u^2-6u-9=0

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

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

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

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

Solving for variable 'u'.

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

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

Ignore the factor 3.
Subproblem 1
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
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 = {-1, 3}