2(9x-6)(3x+4)=0

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Solution for 2(9x-6)(3x+4)=0 equation: 


Simplifying
2(9x + -6)(3x + 4) = 0

Reorder the terms:
2(-6 + 9x)(3x + 4) = 0

Reorder the terms:
2(-6 + 9x)(4 + 3x) = 0

Multiply (-6 + 9x) * (4 + 3x)
2(-6(4 + 3x) + 9x * (4 + 3x)) = 0
2((4 * -6 + 3x * -6) + 9x * (4 + 3x)) = 0
2((-24 + -18x) + 9x * (4 + 3x)) = 0
2(-24 + -18x + (4 * 9x + 3x * 9x)) = 0
2(-24 + -18x + (36x + 27x2)) = 0

Combine like terms: -18x + 36x = 18x
2(-24 + 18x + 27x2) = 0
(-24 * 2 + 18x * 2 + 27x2 * 2) = 0
(-48 + 36x + 54x2) = 0

Solving
-48 + 36x + 54x2 = 0

Solving for variable 'x'.

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

Factor a trinomial.
6((-4 + -3x)(2 + -3x)) = 0

Ignore the factor 6.

Subproblem 1
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

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 = {-1.333333333, 0.6666666667}

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