4x(x+1)(3x-2)=0

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Solution for 4x(x+1)(3x-2)=0 equation: 


Simplifying
4x(x + 1)(3x + -2) = 0

Reorder the terms:
4x(1 + x)(3x + -2) = 0

Reorder the terms:
4x(1 + x)(-2 + 3x) = 0

Multiply (1 + x) * (-2 + 3x)
4x(1(-2 + 3x) + x(-2 + 3x)) = 0
4x((-2 * 1 + 3x * 1) + x(-2 + 3x)) = 0
4x((-2 + 3x) + x(-2 + 3x)) = 0
4x(-2 + 3x + (-2 * x + 3x * x)) = 0
4x(-2 + 3x + (-2x + 3x2)) = 0

Combine like terms: 3x + -2x = 1x
4x(-2 + 1x + 3x2) = 0
(-2 * 4x + 1x * 4x + 3x2 * 4x) = 0
(-8x + 4x2 + 12x3) = 0

Solving
-8x + 4x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-2 + x + 3x2) = 0

Factor a trinomial.
4x((-1 + -1x)(2 + -3x)) = 0

Ignore the factor 4.

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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 3
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 = {0, -1, 0.6666666667}

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