(a-b)x+(a+b)x=2a

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

Simplifying
(a + -1b) * x + (a + b) * x = 2a

Reorder the terms for easier multiplication:
x(a + -1b) + (a + b) * x = 2a
(a * x + -1b * x) + (a + b) * x = 2a
(ax + -1bx) + (a + b) * x = 2a

Reorder the terms for easier multiplication:
ax + -1bx + x(a + b) = 2a
ax + -1bx + (a * x + b * x) = 2a
ax + -1bx + (ax + bx) = 2a

Reorder the terms:
ax + ax + -1bx + bx = 2a

Combine like terms: ax + ax = 2ax
2ax + -1bx + bx = 2a

Combine like terms: -1bx + bx = 0
2ax + 0 = 2a
2ax = 2a

Solving
2ax = 2a

Solving for variable 'a'.

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

Add '-2a' to each side of the equation.
-2a + 2ax = 2a + -2a

Combine like terms: 2a + -2a = 0
-2a + 2ax = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-1 + x) = 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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

Combine like terms: 0 + 1 = 1
x = 1

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

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

Simplifying
0 = 1 + -1x

The solution to this equation could not be determined.

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