Solve for p ap-b=-cp+d

$a p - b = - c p + d$

Step 1

Add $c p$ to both sides of the equation.

$a p - b + c p = d$

Step 2

Add $b$ to both sides of the equation.

$a p + c p = d + b$

Step 3

Factor $p$ out of $a p + c p$ .

Factor $p$ out of $a p$ .

$p a + c p = d + b$

Factor $p$ out of $c p$ .

$p a + p c = d + b$

Factor $p$ out of $p a + p c$ .

$p (a + c) = d + b$

Step 4

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

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

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

Simplify the left side.

Cancel the common factor of $a + c$ .

Cancel the common factor.

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

Divide $p$ by $1$ .

$p = \frac{d}{a + c} + \frac{b}{a + c}$

Simplify the right side.

Combine the numerators over the common denominator.

$p = \frac{d + b}{a + c}$