Solve for x ax+2d=5cx+3b

$a x + 2 d = 5 c x + 3 b$

Subtract $5 c x$ from both sides of the equation.

$a x + 2 d - 5 c x = 3 b$

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

$a x - 5 c x = 3 b - 2 d$

Factor $x$ out of $a x - 5 c x$ .

Factor $x$ out of $a x$ .

$x a - 5 c x = 3 b - 2 d$

Factor $x$ out of $- 5 c x$ .

$x a + x (- 5 c) = 3 b - 2 d$

Factor $x$ out of $x a + x (- 5 c)$ .

$x (a - 5 c) = 3 b - 2 d$

Divide each term in $x (a - 5 c) = 3 b - 2 d$ by $a - 5 c$ and simplify.

Divide each term in $x (a - 5 c) = 3 b - 2 d$ by $a - 5 c$ .

$\frac{x (a - 5 c)}{a - 5 c} = \frac{3 b}{a - 5 c} + \frac{- 2 d}{a - 5 c}$

Simplify the left side.

Cancel the common factor of $a - 5 c$ .

Cancel the common factor.

$\frac{x (a - 5 c)}{a - 5 c} = \frac{3 b}{a - 5 c} + \frac{- 2 d}{a - 5 c}$

Divide $x$ by $1$ .

$x = \frac{3 b}{a - 5 c} + \frac{- 2 d}{a - 5 c}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{3 b}{a - 5 c} - \frac{2 d}{a - 5 c}$

Combine the numerators over the common denominator.

$x = \frac{3 b - 2 d}{a - 5 c}$