(2a^2+b^3)(4a^2-b^3)=

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Solution for (2a^2+b^3)(4a^2-b^3)= equation: 


Simplifying
(2a2 + b3)(4a2 + -1b3) = 0

Multiply (2a2 + b3) * (4a2 + -1b3)
(2a2 * (4a2 + -1b3) + b3(4a2 + -1b3)) = 0
((4a2 * 2a2 + -1b3 * 2a2) + b3(4a2 + -1b3)) = 0

Reorder the terms:
((-2a2b3 + 8a4) + b3(4a2 + -1b3)) = 0
((-2a2b3 + 8a4) + b3(4a2 + -1b3)) = 0
(-2a2b3 + 8a4 + (4a2 * b3 + -1b3 * b3)) = 0
(-2a2b3 + 8a4 + (4a2b3 + -1b6)) = 0

Reorder the terms:
(-2a2b3 + 4a2b3 + 8a4 + -1b6) = 0

Combine like terms: -2a2b3 + 4a2b3 = 2a2b3
(2a2b3 + 8a4 + -1b6) = 0

Solving
2a2b3 + 8a4 + -1b6 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a2 + -1b3)(2a2 + b3) = 0


Subproblem 1
Set the factor '(4a2 + -1b3)' equal to zero and attempt to solve:

Simplifying
4a2 + -1b3 = 0

Solving
4a2 + -1b3 = 0

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

Add 'b3' to each side of the equation.
4a2 + -1b3 + b3 = 0 + b3

Combine like terms: -1b3 + b3 = 0
4a2 + 0 = 0 + b3
4a2 = 0 + b3
Remove the zero:
4a2 = b3

Divide each side by '4'.
a2 = 0.25b3

Simplifying
a2 = 0.25b3

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 '(2a2 + b3)' equal to zero and attempt to solve:

Simplifying
2a2 + b3 = 0

Solving
2a2 + b3 = 0

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

Add '-1b3' to each side of the equation.
2a2 + b3 + -1b3 = 0 + -1b3

Combine like terms: b3 + -1b3 = 0
2a2 + 0 = 0 + -1b3
2a2 = 0 + -1b3
Remove the zero:
2a2 = -1b3

Divide each side by '2'.
a2 = -0.5b3

Simplifying
a2 = -0.5b3

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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