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

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


Simplifying
(2x + 2y2)(3x + -4y2) = 0

Multiply (2x + 2y2) * (3x + -4y2)
(2x * (3x + -4y2) + 2y2 * (3x + -4y2)) = 0
((3x * 2x + -4y2 * 2x) + 2y2 * (3x + -4y2)) = 0

Reorder the terms:
((-8xy2 + 6x2) + 2y2 * (3x + -4y2)) = 0
((-8xy2 + 6x2) + 2y2 * (3x + -4y2)) = 0
(-8xy2 + 6x2 + (3x * 2y2 + -4y2 * 2y2)) = 0
(-8xy2 + 6x2 + (6xy2 + -8y4)) = 0

Reorder the terms:
(-8xy2 + 6xy2 + 6x2 + -8y4) = 0

Combine like terms: -8xy2 + 6xy2 = -2xy2
(-2xy2 + 6x2 + -8y4) = 0

Solving
-2xy2 + 6x2 + -8y4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1xy2 + 3x2 + -4y4) = 0

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

Ignore the factor 2.

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

Simplifying
3x + -4y2 = 0

Solving
3x + -4y2 = 0

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

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

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

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

Simplifying
x = 1.333333333y2

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

Simplifying
x + y2 = 0

Solving
x + y2 = 0

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

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

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

Simplifying
x = -1y2
Solution
x = {1.333333333y2, -1y2}

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