9*x^2+6*x=3

Solution for 9*x^2+6*x=3 equation:

Simplifying
9x2 + 6x = 3

Reorder the terms:
6x + 9x2 = 3

Solving
6x + 9x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 6x + 9x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 6x + 9x2 = 0

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

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve:

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {-1, 0.3333333333}