Solve for a a(2x+3)=9x+15+x

$a (2 x + 3) = 9 x + 15 + x$

Step 1

Add $9 x$ and $x$ .

$a (2 x + 3) = 10 x + 15$

Step 2

Divide each term in $a (2 x + 3) = 10 x + 15$ by $2 x + 3$ and simplify.

Divide each term in $a (2 x + 3) = 10 x + 15$ by $2 x + 3$ .

$\frac{a (2 x + 3)}{2 x + 3} = \frac{10 x}{2 x + 3} + \frac{15}{2 x + 3}$

Simplify the left side.

Cancel the common factor of $2 x + 3$ .

Cancel the common factor.

$\frac{a (2 x + 3)}{2 x + 3} = \frac{10 x}{2 x + 3} + \frac{15}{2 x + 3}$

Divide $a$ by $1$ .

$a = \frac{10 x}{2 x + 3} + \frac{15}{2 x + 3}$

Simplify the right side.

Combine the numerators over the common denominator.

$a = \frac{10 x + 15}{2 x + 3}$

Factor $5$ out of $10 x + 15$ .

Factor $5$ out of $10 x$ .

$a = \frac{5 (2 x) + 15}{2 x + 3}$

Factor $5$ out of $15$ .

$a = \frac{5 (2 x) + 5 (3)}{2 x + 3}$

Factor $5$ out of $5 (2 x) + 5 (3)$ .

$a = \frac{5 (2 x + 3)}{2 x + 3}$

Cancel the common factor of $2 x + 3$ .

Cancel the common factor.

$a = \frac{5 (2 x + 3)}{2 x + 3}$

Divide $5$ by $1$ .

$a = 5$