Solve for x rx+qx-d=gc

$r x + q x - d = g c$

Add $d$ to both sides of the equation.

$r x + q x = g c + d$

Factor $x$ out of $r x + q x$ .

Factor $x$ out of $r x$ .

$x r + q x = g c + d$

Factor $x$ out of $q x$ .

$x r + x q = g c + d$

Factor $x$ out of $x r + x q$ .

$x (r + q) = g c + d$

Divide each term in $x (r + q) = g c + d$ by $r + q$ and simplify.

Divide each term in $x (r + q) = g c + d$ by $r + q$ .

$\frac{x (r + q)}{r + q} = \frac{g c}{r + q} + \frac{d}{r + q}$

Simplify the left side.

Cancel the common factor of $r + q$ .

Cancel the common factor.

$\frac{x (r + q)}{r + q} = \frac{g c}{r + q} + \frac{d}{r + q}$

Divide $x$ by $1$ .

$x = \frac{g c}{r + q} + \frac{d}{r + q}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{g c + d}{r + q}$