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

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


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

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

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

Multiply (3 + 4x) * (-1 + 2x)
x(3(-1 + 2x) + 4x * (-1 + 2x)) = 0
x((-1 * 3 + 2x * 3) + 4x * (-1 + 2x)) = 0
x((-3 + 6x) + 4x * (-1 + 2x)) = 0
x(-3 + 6x + (-1 * 4x + 2x * 4x)) = 0
x(-3 + 6x + (-4x + 8x2)) = 0

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

Solving
-3x + 2x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + 2x + 8x2) = 0

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

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75

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, -0.75, 0.5}

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