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

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


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

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

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

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

Combine like terms: -20x + 6x = -14x
X(-15 + -14x + 8x2) = 0
(-15 * X + -14x * X + 8x2 * X) = 0
(-15X + -14xX + 8x2X) = 0

Solving
-15X + -14xX + 8x2X = 0

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'X'.
X(-15 + -14x + 8x2) = 0

Factor a trinomial.
X((-3 + -4x)(5 + -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 Add '4x' to each side of the equation. -4x + 4x = 3 + 4x Combine like terms: -4x + 4x = 0 0 = 3 + 4x Simplifying 0 = 3 + 4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 3

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 Add '2x' to each side of the equation. -2x + 2x = -5 + 2x Combine like terms: -2x + 2x = 0 0 = -5 + 2x Simplifying 0 = -5 + 2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

X = {0}

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