6u^2+9u+3=0

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

Simplifying
6u2 + 9u + 3 = 0

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

Solving
3 + 9u + 6u2 = 0

Solving for variable 'u'.

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

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

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

Simplifying
1 + u = 0

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

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

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

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

Simplifying
1 + 2u = 0

Solving
1 + 2u = 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 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-1, -0.5}