x=x(a+b)

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

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

Solving
x = ax + bx

Solving for variable 'x'.

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

Add '-1ax' to each side of the equation.
-1ax + x = ax + -1ax + bx

Combine like terms: ax + -1ax = 0
-1ax + x = 0 + bx
-1ax + x = bx

Add '-1bx' to each side of the equation.
-1ax + -1bx + x = bx + -1bx

Combine like terms: bx + -1bx = 0
-1ax + -1bx + x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1a + -1b + 1) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1a + -1b + 1)' equal to zero and attempt to solve:

Simplifying
-1a + -1b + 1 = 0

Reorder the terms:
1 + -1a + -1b = 0

Solving
1 + -1a + -1b = 0

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

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

Reorder the terms:
1 + -1 + -1a + -1b = 0 + -1

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

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

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

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

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

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

Simplifying
0 = -1 + a + b

The solution to this equation could not be determined.

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