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

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


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

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

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

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

Combine like terms: 8x + -1x = 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((-4 + -1x)(1 + -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 + -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

Subproblem 3
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
Solution
x = {0, -4, 0.5}

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