x=ax-dx

Solution for x=ax-dx equation:

Simplifying
x = ax + -1dx

Solving
x = ax + -1dx

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 + -1dx

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

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

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

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

Simplifying
-1a + d + 1 = 0

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

Solving
1 + -1a + d = 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 + d = 0 + -1

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

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

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

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

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

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

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

Simplifying
0 = -1 + a + -1d

The solution to this equation could not be determined.

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