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

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

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

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

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

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

Combine like terms: 3x + -4x = -1x
2x(-4 + -1x + 3x2) = 0
(-4 * 2x + -1x * 2x + 3x2 * 2x) = 0
(-8x + -2x2 + 6x3) = 0

Solving
-8x + -2x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-4 + -1x + 3x2) = 0

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

Ignore the factor 2.
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 '(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, -1, 1.333333333}