0=9x^2+15x+6

Solution for 0=9x^2+15x+6 equation:

Simplifying
0 = 9x2 + 15x + 6

Reorder the terms:
0 = 6 + 15x + 9x2

Solving
0 = 6 + 15x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -15x + -9x2 = 6 + 15x + 9x2 + -6 + -15x + -9x2

Reorder the terms:
-6 + -15x + -9x2 = 6 + -6 + 15x + -15x + 9x2 + -9x2

Combine like terms: 6 + -6 = 0
-6 + -15x + -9x2 = 0 + 15x + -15x + 9x2 + -9x2
-6 + -15x + -9x2 = 15x + -15x + 9x2 + -9x2

Combine like terms: 15x + -15x = 0
-6 + -15x + -9x2 = 0 + 9x2 + -9x2
-6 + -15x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-6 + -15x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(2 + 5x + 3x2) = 0

Factor a trinomial.
-3((1 + x)(2 + 3x)) = 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

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

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

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

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

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