3a+6ab+4a(b+c)=

Solution for 3a+6ab+4a(b+c)= equation:

Simplifying
3a + 6ab + 4a(b + c) = 0
3a + 6ab + (b * 4a + c * 4a) = 0
3a + 6ab + (4ab + 4ac) = 0

Combine like terms: 6ab + 4ab = 10ab
3a + 10ab + 4ac = 0

Solving
3a + 10ab + 4ac = 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), 'a'.
a(3 + 10b + 4c) = 0

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 + 10b + 4c)' equal to zero and attempt to solve:

Simplifying
3 + 10b + 4c = 0

Solving
3 + 10b + 4c = 0

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

Add '-3' to each side of the equation.
3 + 10b + -3 + 4c = 0 + -3

Reorder the terms:
3 + -3 + 10b + 4c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 10b + 4c = 0 + -3
10b + 4c = 0 + -3

Combine like terms: 0 + -3 = -3
10b + 4c = -3

Add '-10b' to each side of the equation.
10b + -10b + 4c = -3 + -10b

Combine like terms: 10b + -10b = 0
0 + 4c = -3 + -10b
4c = -3 + -10b

Add '-4c' to each side of the equation.
4c + -4c = -3 + -10b + -4c

Combine like terms: 4c + -4c = 0
0 = -3 + -10b + -4c

Simplifying
0 = -3 + -10b + -4c

The solution to this equation could not be determined.

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