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

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


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

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

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

Multiply (-3 + 2x) * (1 + 4x)
x(-3(1 + 4x) + 2x * (1 + 4x)) = 0
x((1 * -3 + 4x * -3) + 2x * (1 + 4x)) = 0
x((-3 + -12x) + 2x * (1 + 4x)) = 0
x(-3 + -12x + (1 * 2x + 4x * 2x)) = 0
x(-3 + -12x + (2x + 8x2)) = 0

Combine like terms: -12x + 2x = -10x
x(-3 + -10x + 8x2) = 0
(-3 * x + -10x * x + 8x2 * x) = 0
(-3x + -10x2 + 8x3) = 0

Solving
-3x + -10x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -10x + 8x2) = 0

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


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 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, -0.25, 1.5}

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