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

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


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

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

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

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

Combine like terms: -4xy2 + 3xy2 = -1xy2
(-1xy2 + 2x2 + -6y4) = 0

Solving
-1xy2 + 2x2 + -6y4 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(x + -2y2)' equal to zero and attempt to solve:

Simplifying
x + -2y2 = 0

Solving
x + -2y2 = 0

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

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

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

Simplifying
x = 2y2

Subproblem 2
Set the factor '(2x + 3y2)' equal to zero and attempt to solve:

Simplifying
2x + 3y2 = 0

Solving
2x + 3y2 = 0

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

Add '-3y2' to each side of the equation.
2x + 3y2 + -3y2 = 0 + -3y2

Combine like terms: 3y2 + -3y2 = 0
2x + 0 = 0 + -3y2
2x = 0 + -3y2
Remove the zero:
2x = -3y2

Divide each side by '2'.
x = -1.5y2

Simplifying
x = -1.5y2
Solution
x = {2y2, -1.5y2}

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