0=9x^2-3x-2

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Solution for 0=9x^2-3x-2 equation: 


Simplifying
0 = 9x2 + -3x + -2

Reorder the terms:
0 = -2 + -3x + 9x2

Solving
0 = -2 + -3x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + 3x + -9x2 = -2 + -3x + 9x2 + 2 + 3x + -9x2

Reorder the terms:
2 + 3x + -9x2 = -2 + 2 + -3x + 3x + 9x2 + -9x2

Combine like terms: -2 + 2 = 0
2 + 3x + -9x2 = 0 + -3x + 3x + 9x2 + -9x2
2 + 3x + -9x2 = -3x + 3x + 9x2 + -9x2

Combine like terms: -3x + 3x = 0
2 + 3x + -9x2 = 0 + 9x2 + -9x2
2 + 3x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
2 + 3x + -9x2 = 0

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


Subproblem 1
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

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 = {0.6666666667, -0.3333333333}

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