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

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


Simplifying
(a + -1b2)(4a + 2b2) = 0

Multiply (a + -1b2) * (4a + 2b2)
(a(4a + 2b2) + -1b2 * (4a + 2b2)) = 0
((4a * a + 2b2 * a) + -1b2 * (4a + 2b2)) = 0

Reorder the terms:
((2ab2 + 4a2) + -1b2 * (4a + 2b2)) = 0
((2ab2 + 4a2) + -1b2 * (4a + 2b2)) = 0
(2ab2 + 4a2 + (4a * -1b2 + 2b2 * -1b2)) = 0
(2ab2 + 4a2 + (-4ab2 + -2b4)) = 0

Reorder the terms:
(2ab2 + -4ab2 + 4a2 + -2b4) = 0

Combine like terms: 2ab2 + -4ab2 = -2ab2
(-2ab2 + 4a2 + -2b4) = 0

Solving
-2ab2 + 4a2 + -2b4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ab2 + 2a2 + -1b4) = 0

Factor a trinomial.
2((a + -1b2)(2a + b2)) = 0

Ignore the factor 2.

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

Simplifying
a + -1b2 = 0

Solving
a + -1b2 = 0

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

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

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

Simplifying
a = b2

Subproblem 2
Set the factor '(2a + b2)' equal to zero and attempt to solve:

Simplifying
2a + b2 = 0

Solving
2a + b2 = 0

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

Add '-1b2' to each side of the equation.
2a + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
2a + 0 = 0 + -1b2
2a = 0 + -1b2
Remove the zero:
2a = -1b2

Divide each side by '2'.
a = -0.5b2

Simplifying
a = -0.5b2
Solution
a = {b2, -0.5b2}

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