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

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


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

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

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

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

Combine like terms: 2xy2 + 6xy2 = 8xy2
(8xy2 + 3x2 + 4y4) = 0

Solving
8xy2 + 3x2 + 4y4 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3x + 2y2)' equal to zero and attempt to solve:

Simplifying
3x + 2y2 = 0

Solving
3x + 2y2 = 0

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

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

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

Divide each side by '3'.
x = -0.6666666667y2

Simplifying
x = -0.6666666667y2

Subproblem 2
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
Solution
x = {-0.6666666667y2, -2y2}

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