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

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


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

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

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

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

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

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

Solving for variable 'x'.
Remove the zero:
3x + 10x2 + -8x3 = -3x + -10x2 + 8x3 + 3x + 10x2 + -8x3

Reorder the terms:
3x + 10x2 + -8x3 = -3x + 3x + -10x2 + 10x2 + 8x3 + -8x3

Combine like terms: -3x + 3x = 0
3x + 10x2 + -8x3 = 0 + -10x2 + 10x2 + 8x3 + -8x3
3x + 10x2 + -8x3 = -10x2 + 10x2 + 8x3 + -8x3

Combine like terms: -10x2 + 10x2 = 0
3x + 10x2 + -8x3 = 0 + 8x3 + -8x3
3x + 10x2 + -8x3 = 8x3 + -8x3

Combine like terms: 8x3 + -8x3 = 0
3x + 10x2 + -8x3 = 0

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

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

Subproblem 3
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
Solution
x = {0, 1.5, -0.25}

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