(3x-4)(9x+6)=0

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Solution for (3x-4)(9x+6)=0 equation: 


Simplifying
(3x + -4)(9x + 6) = 0

Reorder the terms:
(-4 + 3x)(9x + 6) = 0

Reorder the terms:
(-4 + 3x)(6 + 9x) = 0

Multiply (-4 + 3x) * (6 + 9x)
(-4(6 + 9x) + 3x * (6 + 9x)) = 0
((6 * -4 + 9x * -4) + 3x * (6 + 9x)) = 0
((-24 + -36x) + 3x * (6 + 9x)) = 0
(-24 + -36x + (6 * 3x + 9x * 3x)) = 0
(-24 + -36x + (18x + 27x2)) = 0

Combine like terms: -36x + 18x = -18x
(-24 + -18x + 27x2) = 0

Solving
-24 + -18x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -6x + 9x2) = 0

Factor a trinomial.
3((-2 + -3x)(4 + -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 '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-0.6666666667, 1.333333333}

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