Solve for x bx-c=ax+d

$b x - c = a x + d$

Subtract $a x$ from both sides of the equation.

$b x - c - a x = d$

Add $c$ to both sides of the equation.

$b x - a x = d + c$

Factor $x$ out of $b x - a x$ .

Factor $x$ out of $b x$ .

$x b - a x = d + c$

Factor $x$ out of $- a x$ .

$x b + x (- a) = d + c$

Factor $x$ out of $x b + x (- a)$ .

$x (b - a) = d + c$

Divide each term in $x (b - a) = d + c$ by $b - a$ and simplify.

Divide each term in $x (b - a) = d + c$ by $b - a$ .

$\frac{x (b - a)}{b - a} = \frac{d}{b - a} + \frac{c}{b - a}$

Simplify the left side.

Cancel the common factor of $b - a$ .

Cancel the common factor.

$\frac{x (b - a)}{b - a} = \frac{d}{b - a} + \frac{c}{b - a}$

Divide $x$ by $1$ .

$x = \frac{d}{b - a} + \frac{c}{b - a}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{d + c}{b - a}$