0=-9x^2+6x+3

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


Simplifying
0 = -9x2 + 6x + 3

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

Solving
0 = 3 + 6x + -9x2

Solving for variable 'x'.

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

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

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

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

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

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

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.3333333333, 1}

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