Solve for x ax+2c=bx+3d

$a x + 2 c = b x + 3 d$

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

$a x + 2 c - b x = 3 d$

Subtract $2 c$ from both sides of the equation.

$a x - b x = 3 d - 2 c$

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

Factor $x$ out of $a x$ .

$x a - b x = 3 d - 2 c$

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

$x a + x (- b) = 3 d - 2 c$

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

$x (a - b) = 3 d - 2 c$

Divide each term in $x (a - b) = 3 d - 2 c$ by $a - b$ and simplify.

Divide each term in $x (a - b) = 3 d - 2 c$ by $a - b$ .

$\frac{x (a - b)}{a - b} = \frac{3 d}{a - b} + \frac{- 2 c}{a - b}$

Simplify the left side.

Cancel the common factor of $a - b$ .

Cancel the common factor.

$\frac{x (a - b)}{a - b} = \frac{3 d}{a - b} + \frac{- 2 c}{a - b}$

Divide $x$ by $1$ .

$x = \frac{3 d}{a - b} + \frac{- 2 c}{a - b}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{3 d}{a - b} - \frac{2 c}{a - b}$

Combine the numerators over the common denominator.

$x = \frac{3 d - 2 c}{a - b}$