ax+b-d=e

Solution for ax+b-d=e equation:

Simplifying
ax + b + -1d = e

Solving
ax + b + -1d = e

Solving for variable 'a'.

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

Add '-1b' to each side of the equation.
ax + b + -1b + -1d = -1b + e

Combine like terms: b + -1b = 0
ax + 0 + -1d = -1b + e
ax + -1d = -1b + e

Add 'd' to each side of the equation.
ax + -1d + d = -1b + d + e

Combine like terms: -1d + d = 0
ax + 0 = -1b + d + e
ax = -1b + d + e

Divide each side by 'x'.
a = -1bx-1 + dx-1 + ex-1

Simplifying
a = -1bx-1 + dx-1 + ex-1