C+ax=dx
this one has all variables and no numbers

That's OK, but you have not said which variable you want to solve it for.

To solve for 'x':
                                           c + ax = dx

Subtract c from each side:    ax = dx - c

Subtract  dx  from each side:   ax - dx = -c

Factor the left side:                 x (a - d) = -c

Divide each side by (a - d) :      x = -c / (a - d)  or  x = c / (d - a) .

To solve for 'c':
                                   c + ax = dx

Subtract  ax  from each side and factor:   c  = x (d - a)

To solve for 'd':
                                      c + ax = dx

Divide each side by 'x':     d = c/x + a .

To solve for 'a':
                                           c + ax = dx

Subtract 'c' from each side:    ax = dx - c

Divide each side by 'x':          a = d - c/x .
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