ax+bcx+d=A

Solution for ax+bcx+d=A equation:

Simplifying
ax + bcx + d = A

Solving
ax + bcx + d = A

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 + d = A + -1bcx

Combine like terms: bcx + -1bcx = 0
ax + 0 + d = A + -1bcx
ax + d = A + -1bcx

Add '-1d' to each side of the equation.
ax + d + -1d = A + -1bcx + -1d

Combine like terms: d + -1d = 0
ax + 0 = A + -1bcx + -1d
ax = A + -1bcx + -1d

Divide each side by 'x'.
a = x-1A + -1bc + -1dx-1

Simplifying
a = x-1A + -1bc + -1dx-1

Reorder the terms:
a = -1bc + -1dx-1 + x-1A