(ab+4a-6)+(ab+6)=0

Solution for (ab+4a-6)+(ab+6)=0 equation:

Simplifying
(ab + 4a + -6) + (ab + 6) = 0

Reorder the terms:
(-6 + 4a + ab) + (ab + 6) = 0

Remove parenthesis around (-6 + 4a + ab)
-6 + 4a + ab + (ab + 6) = 0

Reorder the terms:
-6 + 4a + ab + (6 + ab) = 0

Remove parenthesis around (6 + ab)
-6 + 4a + ab + 6 + ab = 0

Reorder the terms:
-6 + 6 + 4a + ab + ab = 0

Combine like terms: -6 + 6 = 0
0 + 4a + ab + ab = 0
4a + ab + ab = 0

Combine like terms: ab + ab = 2ab
4a + 2ab = 0

Solving
4a + 2ab = 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), '2a'.
2a(2 + b) = 0

Ignore the factor 2.
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 '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 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 + b = 0 + -2

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

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

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

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

Simplifying
0 = -2 + -1b

The solution to this equation could not be determined.

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