a(m+n)=ab

Solution for a(m+n)=ab equation:

Simplifying
a(m + n) = ab
(m * a + n * a) = ab
(am + an) = ab

Solving
am + an = ab

Solving for variable 'a'.

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

Add '-1ab' to each side of the equation.
am + -1ab + an = ab + -1ab

Reorder the terms:
-1ab + am + an = ab + -1ab

Combine like terms: ab + -1ab = 0
-1ab + am + an = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-1b + m + n) = 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 '(-1b + m + n)' equal to zero and attempt to solve:

Simplifying
-1b + m + n = 0

Solving
-1b + m + n = 0

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

Add 'b' to each side of the equation.
-1b + m + b + n = 0 + b

Reorder the terms:
-1b + b + m + n = 0 + b

Combine like terms: -1b + b = 0
0 + m + n = 0 + b
m + n = 0 + b
Remove the zero:
m + n = b

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

Combine like terms: m + -1m = 0
0 + n = b + -1m
n = b + -1m

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

Combine like terms: n + -1n = 0
0 = b + -1m + -1n

Simplifying
0 = b + -1m + -1n

The solution to this equation could not be determined.

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