3x(x+5)(2x-7)(3x-13)=0

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Solution for 3x(x+5)(2x-7)(3x-13)=0 equation: 


Simplifying
3x(x + 5)(2x + -7)(3x + -13) = 0

Reorder the terms:
3x(5 + x)(2x + -7)(3x + -13) = 0

Reorder the terms:
3x(5 + x)(-7 + 2x)(3x + -13) = 0

Reorder the terms:
3x(5 + x)(-7 + 2x)(-13 + 3x) = 0

Multiply (5 + x) * (-7 + 2x)
3x(5(-7 + 2x) + x(-7 + 2x))(-13 + 3x) = 0
3x((-7 * 5 + 2x * 5) + x(-7 + 2x))(-13 + 3x) = 0
3x((-35 + 10x) + x(-7 + 2x))(-13 + 3x) = 0
3x(-35 + 10x + (-7 * x + 2x * x))(-13 + 3x) = 0
3x(-35 + 10x + (-7x + 2x2))(-13 + 3x) = 0

Combine like terms: 10x + -7x = 3x
3x(-35 + 3x + 2x2)(-13 + 3x) = 0

Multiply (-35 + 3x + 2x2) * (-13 + 3x)
3x(-35(-13 + 3x) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0
3x((-13 * -35 + 3x * -35) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0
3x((455 + -105x) + 3x * (-13 + 3x) + 2x2 * (-13 + 3x)) = 0
3x(455 + -105x + (-13 * 3x + 3x * 3x) + 2x2 * (-13 + 3x)) = 0
3x(455 + -105x + (-39x + 9x2) + 2x2 * (-13 + 3x)) = 0
3x(455 + -105x + -39x + 9x2 + (-13 * 2x2 + 3x * 2x2)) = 0
3x(455 + -105x + -39x + 9x2 + (-26x2 + 6x3)) = 0

Combine like terms: -105x + -39x = -144x
3x(455 + -144x + 9x2 + -26x2 + 6x3) = 0

Combine like terms: 9x2 + -26x2 = -17x2
3x(455 + -144x + -17x2 + 6x3) = 0
(455 * 3x + -144x * 3x + -17x2 * 3x + 6x3 * 3x) = 0
(1365x + -432x2 + -51x3 + 18x4) = 0

Solving
1365x + -432x2 + -51x3 + 18x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(455 + -144x + -17x2 + 6x3) = 0

Ignore the factor 3.

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 '(455 + -144x + -17x2 + 6x3)' equal to zero and attempt to solve:

Simplifying
455 + -144x + -17x2 + 6x3 = 0

Solving
455 + -144x + -17x2 + 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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