ax+b=c(x+d)

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

Simplifying
ax + b = c(x + d)

Reorder the terms:
ax + b = c(d + x)
ax + b = (d * c + x * c)
ax + b = (cd + cx)

Solving
ax + b = cd + cx

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 = cd + -1b + cx

Combine like terms: b + -1b = 0
ax + 0 = cd + -1b + cx
ax = cd + -1b + cx

Reorder the terms:
ax = -1b + cd + cx

Divide each side by 'x'.
a = -1bx-1 + cdx-1 + c

Simplifying
a = -1bx-1 + cdx-1 + c

Reorder the terms:
a = -1bx-1 + c + cdx-1