(2v^2+2sy)(2v^2+sy)=

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Solution for (2v^2+2sy)(2v^2+sy)= equation: 


Simplifying
(2v2 + 2sy)(2v2 + sy) = 0

Reorder the terms:
(2sy + 2v2)(2v2 + sy) = 0

Reorder the terms:
(2sy + 2v2)(sy + 2v2) = 0

Multiply (2sy + 2v2) * (sy + 2v2)
(2sy * (sy + 2v2) + 2v2 * (sy + 2v2)) = 0
((sy * 2sy + 2v2 * 2sy) + 2v2 * (sy + 2v2)) = 0

Reorder the terms:
((4sv2y + 2s2y2) + 2v2 * (sy + 2v2)) = 0
((4sv2y + 2s2y2) + 2v2 * (sy + 2v2)) = 0
(4sv2y + 2s2y2 + (sy * 2v2 + 2v2 * 2v2)) = 0
(4sv2y + 2s2y2 + (2sv2y + 4v4)) = 0

Reorder the terms:
(4sv2y + 2sv2y + 2s2y2 + 4v4) = 0

Combine like terms: 4sv2y + 2sv2y = 6sv2y
(6sv2y + 2s2y2 + 4v4) = 0

Solving
6sv2y + 2s2y2 + 4v4 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3sv2y + s2y2 + 2v4) = 0

Factor a trinomial.
2((sy + v2)(sy + 2v2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(sy + v2)' equal to zero and attempt to solve:

Simplifying
sy + v2 = 0

Solving
sy + v2 = 0

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

Add '-1v2' to each side of the equation.
sy + v2 + -1v2 = 0 + -1v2

Combine like terms: v2 + -1v2 = 0
sy + 0 = 0 + -1v2
sy = 0 + -1v2
Remove the zero:
sy = -1v2

Divide each side by 'y'.
s = -1v2y-1

Simplifying
s = -1v2y-1

Subproblem 2
Set the factor '(sy + 2v2)' equal to zero and attempt to solve:

Simplifying
sy + 2v2 = 0

Solving
sy + 2v2 = 0

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

Add '-2v2' to each side of the equation.
sy + 2v2 + -2v2 = 0 + -2v2

Combine like terms: 2v2 + -2v2 = 0
sy + 0 = 0 + -2v2
sy = 0 + -2v2
Remove the zero:
sy = -2v2

Divide each side by 'y'.
s = -2v2y-1

Simplifying
s = -2v2y-1
Solution
s = {-1v2y-1, -2v2y-1}

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