3x(4x-1)(-2x+5)=0

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Solution for 3x(4x-1)(-2x+5)=0 equation:


Simplifying
3x(4x + -1)(-2x + 5) = 0

Reorder the terms:
3x(-1 + 4x)(-2x + 5) = 0

Reorder the terms:
3x(-1 + 4x)(5 + -2x) = 0

Multiply (-1 + 4x) * (5 + -2x)
3x(-1(5 + -2x) + 4x * (5 + -2x)) = 0
3x((5 * -1 + -2x * -1) + 4x * (5 + -2x)) = 0
3x((-5 + 2x) + 4x * (5 + -2x)) = 0
3x(-5 + 2x + (5 * 4x + -2x * 4x)) = 0
3x(-5 + 2x + (20x + -8x2)) = 0

Combine like terms: 2x + 20x = 22x
3x(-5 + 22x + -8x2) = 0
(-5 * 3x + 22x * 3x + -8x2 * 3x) = 0
(-15x + 66x2 + -24x3) = 0

Solving
-15x + 66x2 + -24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-5 + 22x + -8x2) = 0

Factor a trinomial.
3x((-5 + 2x)(1 + -4x)) = 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 '(-5 + 2x)' equal to zero and attempt to solve: Simplifying -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5

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, 2.5, 0.25}

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