(4x^2+5x)(20x^2-3x-2)=0

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Solution for (4x^2+5x)(20x^2-3x-2)=0 equation: 


Simplifying
(4x2 + 5x)(20x2 + -3x + -2) = 0

Reorder the terms:
(5x + 4x2)(20x2 + -3x + -2) = 0

Reorder the terms:
(5x + 4x2)(-2 + -3x + 20x2) = 0

Multiply (5x + 4x2) * (-2 + -3x + 20x2)
(5x * (-2 + -3x + 20x2) + 4x2 * (-2 + -3x + 20x2)) = 0
((-2 * 5x + -3x * 5x + 20x2 * 5x) + 4x2 * (-2 + -3x + 20x2)) = 0
((-10x + -15x2 + 100x3) + 4x2 * (-2 + -3x + 20x2)) = 0
(-10x + -15x2 + 100x3 + (-2 * 4x2 + -3x * 4x2 + 20x2 * 4x2)) = 0
(-10x + -15x2 + 100x3 + (-8x2 + -12x3 + 80x4)) = 0

Reorder the terms:
(-10x + -15x2 + -8x2 + 100x3 + -12x3 + 80x4) = 0

Combine like terms: -15x2 + -8x2 = -23x2
(-10x + -23x2 + 100x3 + -12x3 + 80x4) = 0

Combine like terms: 100x3 + -12x3 = 88x3
(-10x + -23x2 + 88x3 + 80x4) = 0

Solving
-10x + -23x2 + 88x3 + 80x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + -23x + 88x2 + 80x3) = 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 '(-10 + -23x + 88x2 + 80x3)' equal to zero and attempt to solve:

Simplifying
-10 + -23x + 88x2 + 80x3 = 0

Solving
-10 + -23x + 88x2 + 80x3 = 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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