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

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


Simplifying
(x2 + 4x + -5)(2x3 + -3x) = 0

Reorder the terms:
(-5 + 4x + x2)(2x3 + -3x) = 0

Reorder the terms:
(-5 + 4x + x2)(-3x + 2x3) = 0

Multiply (-5 + 4x + x2) * (-3x + 2x3)
(-5(-3x + 2x3) + 4x * (-3x + 2x3) + x2(-3x + 2x3)) = 0
((-3x * -5 + 2x3 * -5) + 4x * (-3x + 2x3) + x2(-3x + 2x3)) = 0
((15x + -10x3) + 4x * (-3x + 2x3) + x2(-3x + 2x3)) = 0
(15x + -10x3 + (-3x * 4x + 2x3 * 4x) + x2(-3x + 2x3)) = 0
(15x + -10x3 + (-12x2 + 8x4) + x2(-3x + 2x3)) = 0
(15x + -10x3 + -12x2 + 8x4 + (-3x * x2 + 2x3 * x2)) = 0
(15x + -10x3 + -12x2 + 8x4 + (-3x3 + 2x5)) = 0

Reorder the terms:
(15x + -12x2 + -10x3 + -3x3 + 8x4 + 2x5) = 0

Combine like terms: -10x3 + -3x3 = -13x3
(15x + -12x2 + -13x3 + 8x4 + 2x5) = 0

Solving
15x + -12x2 + -13x3 + 8x4 + 2x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -12x + -13x2 + 8x3 + 2x4) = 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 '(15 + -12x + -13x2 + 8x3 + 2x4)' equal to zero and attempt to solve: Simplifying 15 + -12x + -13x2 + 8x3 + 2x4 = 0 Solving 15 + -12x + -13x2 + 8x3 + 2x4 = 0 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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