3a(b+c)-a(2b+c)=

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

Simplifying
3a(b + c) + -1a(2b + c) = 0
(b * 3a + c * 3a) + -1a(2b + c) = 0
(3ab + 3ac) + -1a(2b + c) = 0
3ab + 3ac + (2b * -1a + c * -1a) = 0
3ab + 3ac + (-2ab + -1ac) = 0

Reorder the terms:
3ab + -2ab + 3ac + -1ac = 0

Combine like terms: 3ab + -2ab = 1ab
1ab + 3ac + -1ac = 0

Combine like terms: 3ac + -1ac = 2ac
1ab + 2ac = 0

Solving
1ab + 2ac = 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(b + 2c) = 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 '(b + 2c)' equal to zero and attempt to solve:

Simplifying
b + 2c = 0

Solving
b + 2c = 0

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

Add '-1b' to each side of the equation.
b + -1b + 2c = 0 + -1b

Combine like terms: b + -1b = 0
0 + 2c = 0 + -1b
2c = 0 + -1b
Remove the zero:
2c = -1b

Add '-2c' to each side of the equation.
2c + -2c = -1b + -2c

Combine like terms: 2c + -2c = 0
0 = -1b + -2c

Simplifying
0 = -1b + -2c

The solution to this equation could not be determined.

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