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

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


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

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

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

Multiply (1 + 2x) * (-4 + x)
3x(1(-4 + x) + 2x * (-4 + x)) = 0
3x((-4 * 1 + x * 1) + 2x * (-4 + x)) = 0
3x((-4 + 1x) + 2x * (-4 + x)) = 0
3x(-4 + 1x + (-4 * 2x + x * 2x)) = 0
3x(-4 + 1x + (-8x + 2x2)) = 0

Combine like terms: 1x + -8x = -7x
3x(-4 + -7x + 2x2) = 0
(-4 * 3x + -7x * 3x + 2x2 * 3x) = 0
(-12x + -21x2 + 6x3) = 0

Solving
-12x + -21x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + -7x + 2x2) = 0

Factor a trinomial.
3x((-1 + -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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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, -0.5, 4}

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