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

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


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

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

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

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

Combine like terms: 6x + -27x = -21x
(-18 + -21x + 9x2) = 0

Solving
-18 + -21x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -7x + 3x2) = 0

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.6666666667, 3}

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