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

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


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

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

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

Multiply (-3 + 2x) * (4 + 3x)
3x(-3(4 + 3x) + 2x * (4 + 3x)) = 0
3x((4 * -3 + 3x * -3) + 2x * (4 + 3x)) = 0
3x((-12 + -9x) + 2x * (4 + 3x)) = 0
3x(-12 + -9x + (4 * 2x + 3x * 2x)) = 0
3x(-12 + -9x + (8x + 6x2)) = 0

Combine like terms: -9x + 8x = -1x
3x(-12 + -1x + 6x2) = 0
(-12 * 3x + -1x * 3x + 6x2 * 3x) = 0
(-36x + -3x2 + 18x3) = 0

Solving
-36x + -3x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-12 + -1x + 6x2) = 0

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

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -1.333333333, 1.5}

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