4(a)*(b)(2(a)2(b)+8(b))=

Solution for 4(a)*(b)(2(a)2(b)+8(b))= equation:

Simplifying
4(a)(b)(2(a) * 2(b) + 8(b)) = 0

Reorder the terms for easier multiplication:
4a * b(2 * 2a * b + 8(b)) = 0

Multiply 2 * 2
4a * b(4a * b + 8(b)) = 0

Multiply a * b
4a * b(4ab + 8(b)) = 0

Multiply a * b
4ab(4ab + 8b) = 0
(4ab * 4ab + 8b * 4ab) = 0

Reorder the terms:
(32ab2 + 16a2b2) = 0
(32ab2 + 16a2b2) = 0

Solving
32ab2 + 16a2b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '16ab2'.
16ab2(2 + a) = 0

Ignore the factor 16.
Subproblem 1
Set the factor 'ab2' equal to zero and attempt to solve:

Simplifying
ab2 = 0

Solving
ab2 = 0

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

Simplifying
ab2 = 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 '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

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

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

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