(2y+ax^2)(y-2ax^2)=0

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


Simplifying
(2y + ax2)(y + -2ax2) = 0

Reorder the terms:
(ax2 + 2y)(y + -2ax2) = 0

Reorder the terms:
(ax2 + 2y)(-2ax2 + y) = 0

Multiply (ax2 + 2y) * (-2ax2 + y)
(ax2(-2ax2 + y) + 2y * (-2ax2 + y)) = 0
((-2ax2 * ax2 + y * ax2) + 2y * (-2ax2 + y)) = 0

Reorder the terms:
((ax2y + -2a2x4) + 2y * (-2ax2 + y)) = 0
((ax2y + -2a2x4) + 2y * (-2ax2 + y)) = 0
(ax2y + -2a2x4 + (-2ax2 * 2y + y * 2y)) = 0
(ax2y + -2a2x4 + (-4ax2y + 2y2)) = 0

Reorder the terms:
(ax2y + -4ax2y + -2a2x4 + 2y2) = 0

Combine like terms: ax2y + -4ax2y = -3ax2y
(-3ax2y + -2a2x4 + 2y2) = 0

Solving
-3ax2y + -2a2x4 + 2y2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1ax2 + -2y)(2ax2 + -1y) = 0


Subproblem 1
Set the factor '(-1ax2 + -2y)' equal to zero and attempt to solve:

Simplifying
-1ax2 + -2y = 0

Solving
-1ax2 + -2y = 0

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

Add '2y' to each side of the equation.
-1ax2 + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
-1ax2 + 0 = 0 + 2y
-1ax2 = 0 + 2y
Remove the zero:
-1ax2 = 2y

Divide each side by '-1x2'.
a = -2x-2y

Simplifying
a = -2x-2y

Subproblem 2
Set the factor '(2ax2 + -1y)' equal to zero and attempt to solve:

Simplifying
2ax2 + -1y = 0

Solving
2ax2 + -1y = 0

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

Add 'y' to each side of the equation.
2ax2 + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2ax2 + 0 = 0 + y
2ax2 = 0 + y
Remove the zero:
2ax2 = y

Divide each side by '2x2'.
a = 0.5x-2y

Simplifying
a = 0.5x-2y
Solution
a = {-2x-2y, 0.5x-2y}

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