(9x-3)(3x+2)=0

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Solution for (9x-3)(3x+2)=0 equation: 


Simplifying
(9x + -3)(3x + 2) = 0

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

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

Multiply (-3 + 9x) * (2 + 3x)
(-3(2 + 3x) + 9x * (2 + 3x)) = 0
((2 * -3 + 3x * -3) + 9x * (2 + 3x)) = 0
((-6 + -9x) + 9x * (2 + 3x)) = 0
(-6 + -9x + (2 * 9x + 3x * 9x)) = 0
(-6 + -9x + (18x + 27x2)) = 0

Combine like terms: -9x + 18x = 9x
(-6 + 9x + 27x2) = 0

Solving
-6 + 9x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3x + 9x2) = 0

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

Ignore the factor 3.

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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