(6x^3+13x^2-5x)(x^2-5)=0

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Solution for (6x^3+13x^2-5x)(x^2-5)=0 equation: 


Simplifying
(6x3 + 13x2 + -5x)(x2 + -5) = 0

Reorder the terms:
(-5x + 13x2 + 6x3)(x2 + -5) = 0

Reorder the terms:
(-5x + 13x2 + 6x3)(-5 + x2) = 0

Multiply (-5x + 13x2 + 6x3) * (-5 + x2)
(-5x * (-5 + x2) + 13x2 * (-5 + x2) + 6x3 * (-5 + x2)) = 0
((-5 * -5x + x2 * -5x) + 13x2 * (-5 + x2) + 6x3 * (-5 + x2)) = 0
((25x + -5x3) + 13x2 * (-5 + x2) + 6x3 * (-5 + x2)) = 0
(25x + -5x3 + (-5 * 13x2 + x2 * 13x2) + 6x3 * (-5 + x2)) = 0
(25x + -5x3 + (-65x2 + 13x4) + 6x3 * (-5 + x2)) = 0
(25x + -5x3 + -65x2 + 13x4 + (-5 * 6x3 + x2 * 6x3)) = 0
(25x + -5x3 + -65x2 + 13x4 + (-30x3 + 6x5)) = 0

Reorder the terms:
(25x + -65x2 + -5x3 + -30x3 + 13x4 + 6x5) = 0

Combine like terms: -5x3 + -30x3 = -35x3
(25x + -65x2 + -35x3 + 13x4 + 6x5) = 0

Solving
25x + -65x2 + -35x3 + 13x4 + 6x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(25 + -65x + -35x2 + 13x3 + 6x4) = 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 '(25 + -65x + -35x2 + 13x3 + 6x4)' equal to zero and attempt to solve:

Simplifying
25 + -65x + -35x2 + 13x3 + 6x4 = 0

Solving
25 + -65x + -35x2 + 13x3 + 6x4 = 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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