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

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


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

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

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

Multiply (-3 + x) * (1 + 4x)
2x(-3(1 + 4x) + x(1 + 4x)) = 0
2x((1 * -3 + 4x * -3) + x(1 + 4x)) = 0
2x((-3 + -12x) + x(1 + 4x)) = 0
2x(-3 + -12x + (1 * x + 4x * x)) = 0
2x(-3 + -12x + (1x + 4x2)) = 0

Combine like terms: -12x + 1x = -11x
2x(-3 + -11x + 4x2) = 0
(-3 * 2x + -11x * 2x + 4x2 * 2x) = 0
(-6x + -22x2 + 8x3) = 0

Solving
-6x + -22x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-3 + -11x + 4x2) = 0

Factor a trinomial.
2x((-1 + -4x)(3 + -1x)) = 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 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

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

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -0.25, 3}

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