(6x^3-8y^2)(4x^3+2y^2)=0

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Solution for (6x^3-8y^2)(4x^3+2y^2)=0 equation: 


Simplifying
(6x3 + -8y2)(4x3 + 2y2) = 0

Multiply (6x3 + -8y2) * (4x3 + 2y2)
(6x3 * (4x3 + 2y2) + -8y2 * (4x3 + 2y2)) = 0
((4x3 * 6x3 + 2y2 * 6x3) + -8y2 * (4x3 + 2y2)) = 0

Reorder the terms:
((12x3y2 + 24x6) + -8y2 * (4x3 + 2y2)) = 0
((12x3y2 + 24x6) + -8y2 * (4x3 + 2y2)) = 0
(12x3y2 + 24x6 + (4x3 * -8y2 + 2y2 * -8y2)) = 0
(12x3y2 + 24x6 + (-32x3y2 + -16y4)) = 0

Reorder the terms:
(12x3y2 + -32x3y2 + 24x6 + -16y4) = 0

Combine like terms: 12x3y2 + -32x3y2 = -20x3y2
(-20x3y2 + 24x6 + -16y4) = 0

Solving
-20x3y2 + 24x6 + -16y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5x3y2 + 6x6 + -4y4) = 0

Factor a trinomial.
4((3x3 + -4y2)(2x3 + y2)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3x3 + -4y2)' equal to zero and attempt to solve:

Simplifying
3x3 + -4y2 = 0

Solving
3x3 + -4y2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '4y2' to each side of the equation.
3x3 + -4y2 + 4y2 = 0 + 4y2

Combine like terms: -4y2 + 4y2 = 0
3x3 + 0 = 0 + 4y2
3x3 = 0 + 4y2
Remove the zero:
3x3 = 4y2

Divide each side by '3'.
x3 = 1.333333333y2

Simplifying
x3 = 1.333333333y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2x3 + y2)' equal to zero and attempt to solve:

Simplifying
2x3 + y2 = 0

Solving
2x3 + y2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1y2' to each side of the equation.
2x3 + y2 + -1y2 = 0 + -1y2

Combine like terms: y2 + -1y2 = 0
2x3 + 0 = 0 + -1y2
2x3 = 0 + -1y2
Remove the zero:
2x3 = -1y2

Divide each side by '2'.
x3 = -0.5y2

Simplifying
x3 = -0.5y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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