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

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


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

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

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

Multiply (5 + 4x) * (-3 + 2x)
x(5(-3 + 2x) + 4x * (-3 + 2x)) = 0
x((-3 * 5 + 2x * 5) + 4x * (-3 + 2x)) = 0
x((-15 + 10x) + 4x * (-3 + 2x)) = 0
x(-15 + 10x + (-3 * 4x + 2x * 4x)) = 0
x(-15 + 10x + (-12x + 8x2)) = 0

Combine like terms: 10x + -12x = -2x
x(-15 + -2x + 8x2) = 0
(-15 * x + -2x * x + 8x2 * x) = 0
(-15x + -2x2 + 8x3) = 0

Solving
-15x + -2x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-15 + -2x + 8x2) = 0

Factor a trinomial.
x((-5 + -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 '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 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 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25

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, -1.25, 1.5}

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