5x(2x+9)(3x-8)(x+5)=0

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Solution for 5x(2x+9)(3x-8)(x+5)=0 equation: 


Simplifying
5x(2x + 9)(3x + -8)(x + 5) = 0

Reorder the terms:
5x(9 + 2x)(3x + -8)(x + 5) = 0

Reorder the terms:
5x(9 + 2x)(-8 + 3x)(x + 5) = 0

Reorder the terms:
5x(9 + 2x)(-8 + 3x)(5 + x) = 0

Multiply (9 + 2x) * (-8 + 3x)
5x(9(-8 + 3x) + 2x * (-8 + 3x))(5 + x) = 0
5x((-8 * 9 + 3x * 9) + 2x * (-8 + 3x))(5 + x) = 0
5x((-72 + 27x) + 2x * (-8 + 3x))(5 + x) = 0
5x(-72 + 27x + (-8 * 2x + 3x * 2x))(5 + x) = 0
5x(-72 + 27x + (-16x + 6x2))(5 + x) = 0

Combine like terms: 27x + -16x = 11x
5x(-72 + 11x + 6x2)(5 + x) = 0

Multiply (-72 + 11x + 6x2) * (5 + x)
5x(-72(5 + x) + 11x * (5 + x) + 6x2 * (5 + x)) = 0
5x((5 * -72 + x * -72) + 11x * (5 + x) + 6x2 * (5 + x)) = 0
5x((-360 + -72x) + 11x * (5 + x) + 6x2 * (5 + x)) = 0
5x(-360 + -72x + (5 * 11x + x * 11x) + 6x2 * (5 + x)) = 0
5x(-360 + -72x + (55x + 11x2) + 6x2 * (5 + x)) = 0
5x(-360 + -72x + 55x + 11x2 + (5 * 6x2 + x * 6x2)) = 0
5x(-360 + -72x + 55x + 11x2 + (30x2 + 6x3)) = 0

Combine like terms: -72x + 55x = -17x
5x(-360 + -17x + 11x2 + 30x2 + 6x3) = 0

Combine like terms: 11x2 + 30x2 = 41x2
5x(-360 + -17x + 41x2 + 6x3) = 0
(-360 * 5x + -17x * 5x + 41x2 * 5x + 6x3 * 5x) = 0
(-1800x + -85x2 + 205x3 + 30x4) = 0

Solving
-1800x + -85x2 + 205x3 + 30x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-360 + -17x + 41x2 + 6x3) = 0

Ignore the factor 5.

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 '(-360 + -17x + 41x2 + 6x3)' equal to zero and attempt to solve:

Simplifying
-360 + -17x + 41x2 + 6x3 = 0

Solving
-360 + -17x + 41x2 + 6x3 = 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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