0=9*x^2-6*x

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


Simplifying
0 = 9x2 + -6x

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

Solving
0 = -6x + 9x2

Solving for variable 'x'.
Remove the zero:
6x + -9x2 = -6x + 9x2 + 6x + -9x2

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

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

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

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

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 0.6666666667}

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