(a^2+b^2)(a^2-4b^2)=

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Solution for (a^2+b^2)(a^2-4b^2)= equation: 


Simplifying
(a2 + b2)(a2 + -4b2) = 0

Multiply (a2 + b2) * (a2 + -4b2)
(a2(a2 + -4b2) + b2(a2 + -4b2)) = 0
((a2 * a2 + -4b2 * a2) + b2(a2 + -4b2)) = 0

Reorder the terms:
((-4a2b2 + a4) + b2(a2 + -4b2)) = 0
((-4a2b2 + a4) + b2(a2 + -4b2)) = 0
(-4a2b2 + a4 + (a2 * b2 + -4b2 * b2)) = 0
(-4a2b2 + a4 + (a2b2 + -4b4)) = 0

Reorder the terms:
(-4a2b2 + a2b2 + a4 + -4b4) = 0

Combine like terms: -4a2b2 + a2b2 = -3a2b2
(-3a2b2 + a4 + -4b4) = 0

Solving
-3a2b2 + a4 + -4b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(a2 + -4b2)(a2 + b2) = 0

Factor a difference between two squares.
((a + 2b)(a + -2b))(a2 + b2) = 0


Subproblem 1
Set the factor '(a2 + b2)' equal to zero and attempt to solve:

Simplifying
a2 + b2 = 0

Solving
a2 + b2 = 0

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

Add '-1b2' to each side of the equation.
a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
a2 + 0 = 0 + -1b2
a2 = 0 + -1b2
Remove the zero:
a2 = -1b2

Simplifying
a2 = -1b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
a + 2b = 0

Solving
a + 2b = 0

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

Add '-2b' to each side of the equation.
a + 2b + -2b = 0 + -2b

Combine like terms: 2b + -2b = 0
a + 0 = 0 + -2b
a = 0 + -2b
Remove the zero:
a = -2b

Simplifying
a = -2b

Subproblem 3
Set the factor '(a + -2b)' equal to zero and attempt to solve:

Simplifying
a + -2b = 0

Solving
a + -2b = 0

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

Add '2b' to each side of the equation.
a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
a + 0 = 0 + 2b
a = 0 + 2b
Remove the zero:
a = 2b

Simplifying
a = 2b
Solution
a = {-2b, 2b}

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