4[3a-4a(2a+5b)+8a^2]=

Solution for 4[3a-4a(2a+5b)+8a^2]= equation:

Simplifying
4[3a + -4a(2a + 5b) + 8a2] = 0
4[3a + (2a * -4a + 5b * -4a) + 8a2] = 0

Reorder the terms:
4[3a + (-20ab + -8a2) + 8a2] = 0
4[3a + (-20ab + -8a2) + 8a2] = 0

Combine like terms: -8a2 + 8a2 = 0
4[3a + -20ab + 0] = 0
4[3a + -20ab] = 0
[3a * 4 + -20ab * 4] = 0
[12a + -80ab] = 0

Solving
12a + -80ab = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), '4a'.
4a(3 + -20b) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(3 + -20b)' equal to zero and attempt to solve:

Simplifying
3 + -20b = 0

Solving
3 + -20b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -20b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -20b = 0 + -3
-20b = 0 + -3

Combine like terms: 0 + -3 = -3
-20b = -3

Add '20b' to each side of the equation.
-20b + 20b = -3 + 20b

Combine like terms: -20b + 20b = 0
0 = -3 + 20b

Simplifying
0 = -3 + 20b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}