x*(4-3x)(2x-5)=0

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


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

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

Multiply (4 + -3x) * (-5 + 2x)
x(4(-5 + 2x) + -3x * (-5 + 2x)) = 0
x((-5 * 4 + 2x * 4) + -3x * (-5 + 2x)) = 0
x((-20 + 8x) + -3x * (-5 + 2x)) = 0
x(-20 + 8x + (-5 * -3x + 2x * -3x)) = 0
x(-20 + 8x + (15x + -6x2)) = 0

Combine like terms: 8x + 15x = 23x
x(-20 + 23x + -6x2) = 0
(-20 * x + 23x * x + -6x2 * x) = 0
(-20x + 23x2 + -6x3) = 0

Solving
-20x + 23x2 + -6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20 + 23x + -6x2) = 0

Factor a trinomial.
x((-5 + 2x)(4 + -3x)) = 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 '(-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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333

Solution

x = {0, 2.5, 1.333333333}

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