x=ax-dx

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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}

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