(8x-4av^2)(x+av^2)=

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Solution for (8x-4av^2)(x+av^2)= equation: 


Simplifying
(8x + -4av2)(x + av2) = 0

Reorder the terms:
(-4av2 + 8x)(x + av2) = 0

Reorder the terms:
(-4av2 + 8x)(av2 + x) = 0

Multiply (-4av2 + 8x) * (av2 + x)
(-4av2 * (av2 + x) + 8x * (av2 + x)) = 0
((av2 * -4av2 + x * -4av2) + 8x * (av2 + x)) = 0

Reorder the terms:
((-4av2x + -4a2v4) + 8x * (av2 + x)) = 0
((-4av2x + -4a2v4) + 8x * (av2 + x)) = 0
(-4av2x + -4a2v4 + (av2 * 8x + x * 8x)) = 0
(-4av2x + -4a2v4 + (8av2x + 8x2)) = 0

Reorder the terms:
(-4av2x + 8av2x + -4a2v4 + 8x2) = 0

Combine like terms: -4av2x + 8av2x = 4av2x
(4av2x + -4a2v4 + 8x2) = 0

Solving
4av2x + -4a2v4 + 8x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(av2x + -1a2v4 + 2x2) = 0

Factor a trinomial.
4((-1av2 + -1x)(av2 + -2x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-1av2 + -1x)' equal to zero and attempt to solve:

Simplifying
-1av2 + -1x = 0

Solving
-1av2 + -1x = 0

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

Add 'x' to each side of the equation.
-1av2 + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-1av2 + 0 = 0 + x
-1av2 = 0 + x
Remove the zero:
-1av2 = x

Divide each side by '-1v2'.
a = -1v-2x

Simplifying
a = -1v-2x

Subproblem 2
Set the factor '(av2 + -2x)' equal to zero and attempt to solve:

Simplifying
av2 + -2x = 0

Solving
av2 + -2x = 0

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

Add '2x' to each side of the equation.
av2 + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
av2 + 0 = 0 + 2x
av2 = 0 + 2x
Remove the zero:
av2 = 2x

Divide each side by 'v2'.
a = 2v-2x

Simplifying
a = 2v-2x
Solution
a = {-1v-2x, 2v-2x}

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