ax+b(x+c)=dx

Solution for ax+b(x+c)=dx equation:

Simplifying
ax + b(x + c) = dx

Reorder the terms:
ax + b(c + x) = dx
ax + (c * b + x * b) = dx
ax + (bc + bx) = dx

Solving
ax + bc + bx = dx

Solving for variable 'a'.

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

Add '-1bc' to each side of the equation.
ax + bc + -1bc + bx = -1bc + dx

Combine like terms: bc + -1bc = 0
ax + 0 + bx = -1bc + dx
ax + bx = -1bc + dx

Add '-1bx' to each side of the equation.
ax + bx + -1bx = -1bc + -1bx + dx

Combine like terms: bx + -1bx = 0
ax + 0 = -1bc + -1bx + dx
ax = -1bc + -1bx + dx

Divide each side by 'x'.
a = -1bcx-1 + -1b + d

Simplifying
a = -1bcx-1 + -1b + d

Reorder the terms:
a = -1b + -1bcx-1 + d