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

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


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

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

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

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

Combine like terms: -8x + 3x = -5x
3x(-12 + -5x + 2x2) = 0
(-12 * 3x + -5x * 3x + 2x2 * 3x) = 0
(-36x + -15x2 + 6x3) = 0

Solving
-36x + -15x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-12 + -5x + 2x2) = 0

Factor a trinomial.
3x((-3 + -2x)(4 + -1x)) = 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 '(-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

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -1.5, 4}

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