ax+b(cx-d)=e-f(gx-h)

Solution for ax+b(cx-d)=e-f(gx-h) equation:

Simplifying
ax + b(cx + -1d) = e + -1f(gx + -1h)
ax + (cx * b + -1d * b) = e + -1f(gx + -1h)
ax + (bcx + -1bd) = e + -1f(gx + -1h)
ax + bcx + -1bd = e + (gx * -1f + -1h * -1f)
ax + bcx + -1bd = e + (-1fgx + 1fh)

Solving
ax + bcx + -1bd = e + -1fgx + 1fh

Solving for variable 'a'.

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

Add '-1bcx' to each side of the equation.
ax + bcx + -1bcx + -1bd = e + -1fgx + -1bcx + 1fh

Combine like terms: bcx + -1bcx = 0
ax + 0 + -1bd = e + -1fgx + -1bcx + 1fh
ax + -1bd = e + -1fgx + -1bcx + 1fh

Reorder the terms:
ax + -1bd = -1bcx + e + -1fgx + 1fh

Add 'bd' to each side of the equation.
ax + -1bd + bd = -1bcx + e + -1fgx + bd + 1fh

Combine like terms: -1bd + bd = 0
ax + 0 = -1bcx + e + -1fgx + bd + 1fh
ax = -1bcx + e + -1fgx + bd + 1fh

Reorder the terms:
ax = -1bcx + bd + e + -1fgx + 1fh

Divide each side by 'x'.
a = -1bc + bdx-1 + ex-1 + -1fg + fhx-1

Simplifying
a = -1bc + bdx-1 + ex-1 + -1fg + fhx-1