(s+2t^2)(2s-2t^2)=

Solution for (s+2t^2)(2s-2t^2)= equation:

Simplifying
(s + 2t2)(2s + -2t2) = 0

Multiply (s + 2t2) * (2s + -2t2)
(s(2s + -2t2) + 2t2 * (2s + -2t2)) = 0
((2s * s + -2t2 * s) + 2t2 * (2s + -2t2)) = 0

Reorder the terms:
((-2st2 + 2s2) + 2t2 * (2s + -2t2)) = 0
((-2st2 + 2s2) + 2t2 * (2s + -2t2)) = 0
(-2st2 + 2s2 + (2s * 2t2 + -2t2 * 2t2)) = 0
(-2st2 + 2s2 + (4st2 + -4t4)) = 0

Reorder the terms:
(-2st2 + 4st2 + 2s2 + -4t4) = 0

Combine like terms: -2st2 + 4st2 = 2st2
(2st2 + 2s2 + -4t4) = 0

Solving
2st2 + 2s2 + -4t4 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(st2 + s2 + -2t4) = 0

Factor a trinomial.
2((s + -1t2)(s + 2t2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(s + -1t2)' equal to zero and attempt to solve:

Simplifying
s + -1t2 = 0

Solving
s + -1t2 = 0

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

Add 't2' to each side of the equation.
s + -1t2 + t2 = 0 + t2

Combine like terms: -1t2 + t2 = 0
s + 0 = 0 + t2
s = 0 + t2
Remove the zero:
s = t2

Simplifying
s = t2
Subproblem 2
Set the factor '(s + 2t2)' equal to zero and attempt to solve:

Simplifying
s + 2t2 = 0

Solving
s + 2t2 = 0

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

Add '-2t2' to each side of the equation.
s + 2t2 + -2t2 = 0 + -2t2

Combine like terms: 2t2 + -2t2 = 0
s + 0 = 0 + -2t2
s = 0 + -2t2
Remove the zero:
s = -2t2

Simplifying
s = -2t2
Solution
s = {t2, -2t2}