ax+b+(a(x+b))=b

Solution for ax+b+(a(x+b))=b equation:

Simplifying
ax + b + (a(x + b)) = b

Reorder the terms:
ax + b + (a(b + x)) = b
ax + b + ((b * a + x * a)) = b
ax + b + ((ab + ax)) = b
ax + b + (ab + ax) = b

Remove parenthesis around (ab + ax)
ax + b + ab + ax = b

Reorder the terms:
ab + ax + ax + b = b

Combine like terms: ax + ax = 2ax
ab + 2ax + b = b

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

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

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

Solving
ab + 2ax = 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 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
b + 2x = 0

Solving
b + 2x = 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 + 2x = 0 + -1b

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

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

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

Simplifying
0 = -1b + -2x

The solution to this equation could not be determined.

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