Solve for a 18a-9=5(2a+3)

$18 a - 9 = 5 (2 a + 3)$

Step 1

Simplify $5 (2 a + 3)$ .

Rewrite.

$18 a - 9 = 0 + 0 + 5 (2 a + 3)$

Simplify by adding zeros.

$18 a - 9 = 5 (2 a + 3)$

Apply the distributive property.

$18 a - 9 = 5 (2 a) + 5 \cdot 3$

Multiply.

Multiply $2$ by $5$ .

$18 a - 9 = 10 a + 5 \cdot 3$

Multiply $5$ by $3$ .

$18 a - 9 = 10 a + 15$

Step 2

Move all terms containing $a$ to the left side of the equation.

Subtract $10 a$ from both sides of the equation.

$18 a - 9 - 10 a = 15$

Subtract $10 a$ from $18 a$ .

$8 a - 9 = 15$

Step 3

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

Add $9$ to both sides of the equation.

$8 a = 15 + 9$

Add $15$ and $9$ .

$8 a = 24$

Step 4

Divide each term in $8 a = 24$ by $8$ and simplify.

Divide each term in $8 a = 24$ by $8$ .

$\frac{8 a}{8} = \frac{24}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 a}{8} = \frac{24}{8}$

Divide $a$ by $1$ .

$a = \frac{24}{8}$

Simplify the right side.

Divide $24$ by $8$ .

$a = 3$