ax+by-z=c

Solution for ax+by-z=c equation:

Simplifying
ax + by + -1z = c

Solving
ax + by + -1z = c

Solving for variable 'a'.

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

Add '-1by' to each side of the equation.
ax + by + -1by + -1z = -1by + c

Combine like terms: by + -1by = 0
ax + 0 + -1z = -1by + c
ax + -1z = -1by + c

Add 'z' to each side of the equation.
ax + -1z + z = -1by + c + z

Combine like terms: -1z + z = 0
ax + 0 = -1by + c + z
ax = -1by + c + z

Divide each side by 'x'.
a = -1bx-1y + cx-1 + x-1z

Simplifying
a = -1bx-1y + cx-1 + x-1z