Solve for a 3ab-15b-7a+35=0

$3 a b - 15 b - 7 a + 35 = 0$

Step 1

Move all terms not containing $a$ to the right side of the equation.

Add $15 b$ to both sides of the equation.

$3 a b - 7 a + 35 = 15 b$

Subtract $35$ from both sides of the equation.

$3 a b - 7 a = 15 b - 35$

Step 2

Factor $a$ out of $3 a b - 7 a$ .

Factor $a$ out of $3 a b$ .

$a (3 b) - 7 a = 15 b - 35$

Factor $a$ out of $- 7 a$ .

$a (3 b) + a \cdot - 7 = 15 b - 35$

Factor $a$ out of $a (3 b) + a \cdot - 7$ .

$a (3 b - 7) = 15 b - 35$

Step 3

Divide each term in $a (3 b - 7) = 15 b - 35$ by $3 b - 7$ and simplify.

Divide each term in $a (3 b - 7) = 15 b - 35$ by $3 b - 7$ .

$\frac{a (3 b - 7)}{3 b - 7} = \frac{15 b}{3 b - 7} + \frac{- 35}{3 b - 7}$

Simplify the left side.

Cancel the common factor of $3 b - 7$ .

Cancel the common factor.

$\frac{a (3 b - 7)}{3 b - 7} = \frac{15 b}{3 b - 7} + \frac{- 35}{3 b - 7}$

Divide $a$ by $1$ .

$a = \frac{15 b}{3 b - 7} + \frac{- 35}{3 b - 7}$

Simplify the right side.

Combine the numerators over the common denominator.

$a = \frac{15 b - 35}{3 b - 7}$

Factor $5$ out of $15 b - 35$ .

Factor $5$ out of $15 b$ .

$a = \frac{5 (3 b) - 35}{3 b - 7}$

Factor $5$ out of $- 35$ .

$a = \frac{5 (3 b) + 5 (- 7)}{3 b - 7}$

Factor $5$ out of $5 (3 b) + 5 (- 7)$ .

$a = \frac{5 (3 b - 7)}{3 b - 7}$

Cancel the common factor of $3 b - 7$ .

Cancel the common factor.

$a = \frac{5 (3 b - 7)}{3 b - 7}$

Divide $5$ by $1$ .

$a = 5$