Solve for a (4d)/a-9=g

$\frac{4 d}{a} - 9 = g$

Add $9$ to both sides of the equation.

$\frac{4 d}{a} = g + 9$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a, 1, 1$

The LCM of one and any expression is the expression.

$a$

Multiply each term in $\frac{4 d}{a} = g + 9$ by $a$ to eliminate the fractions.

Multiply each term in $\frac{4 d}{a} = g + 9$ by $a$ .

$\frac{4 d}{a} a = g a + 9 a$

Simplify the left side.

Cancel the common factor of $a$ .

Cancel the common factor.

$\frac{4 d}{a} a = g a + 9 a$

Rewrite the expression.

$4 d = g a + 9 a$

Solve the equation.

Rewrite the equation as $g a + 9 a = 4 d$ .

$g a + 9 a = 4 d$

Factor $a$ out of $g a + 9 a$ .

Factor $a$ out of $g a$ .

$a g + 9 a = 4 d$

Factor $a$ out of $9 a$ .

$a g + a \cdot 9 = 4 d$

Factor $a$ out of $a g + a \cdot 9$ .

$a (g + 9) = 4 d$

Divide each term in $a (g + 9) = 4 d$ by $g + 9$ and simplify.

Divide each term in $a (g + 9) = 4 d$ by $g + 9$ .

$\frac{a (g + 9)}{g + 9} = \frac{4 d}{g + 9}$

Simplify the left side.

Cancel the common factor of $g + 9$ .

Cancel the common factor.

$\frac{a (g + 9)}{g + 9} = \frac{4 d}{g + 9}$

Divide $a$ by $1$ .

$a = \frac{4 d}{g + 9}$