((6x^2)+9x+3)=0

Solution for ((6x^2)+9x+3)=0 equation:

Simplifying
((6x2) + 9x + 3) = 0

Reorder the terms:
(3 + 9x + (6x2)) = 0

Remove parenthesis around (3 + 9x + (6x2))
3 + 9x + (6x2) = 0

Solving
3 + 9x + (6x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 3x + (2x2)) = 0

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

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

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

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

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

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