(4u+3as^2)(2u-2as^2)=0

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Solution for (4u+3as^2)(2u-2as^2)=0 equation: 


Simplifying
(4u + 3as2)(2u + -2as2) = 0

Reorder the terms:
(3as2 + 4u)(2u + -2as2) = 0

Reorder the terms:
(3as2 + 4u)(-2as2 + 2u) = 0

Multiply (3as2 + 4u) * (-2as2 + 2u)
(3as2 * (-2as2 + 2u) + 4u * (-2as2 + 2u)) = 0
((-2as2 * 3as2 + 2u * 3as2) + 4u * (-2as2 + 2u)) = 0

Reorder the terms:
((6as2u + -6a2s4) + 4u * (-2as2 + 2u)) = 0
((6as2u + -6a2s4) + 4u * (-2as2 + 2u)) = 0
(6as2u + -6a2s4 + (-2as2 * 4u + 2u * 4u)) = 0
(6as2u + -6a2s4 + (-8as2u + 8u2)) = 0

Reorder the terms:
(6as2u + -8as2u + -6a2s4 + 8u2) = 0

Combine like terms: 6as2u + -8as2u = -2as2u
(-2as2u + -6a2s4 + 8u2) = 0

Solving
-2as2u + -6a2s4 + 8u2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1as2u + -3a2s4 + 4u2) = 0

Factor a trinomial.
2((-3as2 + -4u)(as2 + -1u)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3as2 + -4u)' equal to zero and attempt to solve:

Simplifying
-3as2 + -4u = 0

Solving
-3as2 + -4u = 0

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

Add '4u' to each side of the equation.
-3as2 + -4u + 4u = 0 + 4u

Combine like terms: -4u + 4u = 0
-3as2 + 0 = 0 + 4u
-3as2 = 0 + 4u
Remove the zero:
-3as2 = 4u

Divide each side by '-3s2'.
a = -1.333333333s-2u

Simplifying
a = -1.333333333s-2u

Subproblem 2
Set the factor '(as2 + -1u)' equal to zero and attempt to solve:

Simplifying
as2 + -1u = 0

Solving
as2 + -1u = 0

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

Add 'u' to each side of the equation.
as2 + -1u + u = 0 + u

Combine like terms: -1u + u = 0
as2 + 0 = 0 + u
as2 = 0 + u
Remove the zero:
as2 = u

Divide each side by 's2'.
a = s-2u

Simplifying
a = s-2u
Solution
a = {-1.333333333s-2u, s-2u}

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