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

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

Simplifying
(4a3 + 2b3) + -1(3a2b + -4ab2 + 2b3 + 4a3) = 0

Remove parenthesis around (4a3 + 2b3)
4a3 + 2b3 + -1(3a2b + -4ab2 + 2b3 + 4a3) = 0

Reorder the terms:
4a3 + 2b3 + -1(-4ab2 + 3a2b + 4a3 + 2b3) = 0
4a3 + 2b3 + (-4ab2 * -1 + 3a2b * -1 + 4a3 * -1 + 2b3 * -1) = 0
4a3 + 2b3 + (4ab2 + -3a2b + -4a3 + -2b3) = 0

Reorder the terms:
4ab2 + -3a2b + 4a3 + -4a3 + 2b3 + -2b3 = 0

Combine like terms: 4a3 + -4a3 = 0
4ab2 + -3a2b + 0 + 2b3 + -2b3 = 0
4ab2 + -3a2b + 2b3 + -2b3 = 0

Combine like terms: 2b3 + -2b3 = 0
4ab2 + -3a2b + 0 = 0
4ab2 + -3a2b = 0

Solving
4ab2 + -3a2b = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'ab'.
ab(4b + -3a) = 0

Subproblem 1
Set the factor 'ab' equal to zero and attempt to solve:

Simplifying
ab = 0

Solving
ab = 0

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

Simplifying
ab = 0

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 '(4b + -3a)' equal to zero and attempt to solve:

Simplifying
4b + -3a = 0

Reorder the terms:
-3a + 4b = 0

Solving
-3a + 4b = 0

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

Add '-4b' to each side of the equation.
-3a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-3a + 0 = 0 + -4b
-3a = 0 + -4b
Remove the zero:
-3a = -4b

Divide each side by '-3'.
a = 1.333333333b

Simplifying
a = 1.333333333b
Solution
a = {1.333333333b}