Solve for a 2(4a-12)+3a=6a+1

$2 (4 a - 12) + 3 a = 6 a + 1$

Step 1

Simplify $2 (4 a - 12) + 3 a$ .

Simplify each term.

Apply the distributive property.

$2 (4 a) + 2 \cdot - 12 + 3 a = 6 a + 1$

Multiply $4$ by $2$ .

$8 a + 2 \cdot - 12 + 3 a = 6 a + 1$

Multiply $2$ by $- 12$ .

$8 a - 24 + 3 a = 6 a + 1$

Add $8 a$ and $3 a$ .

$11 a - 24 = 6 a + 1$

Step 2

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

Subtract $6 a$ from both sides of the equation.

$11 a - 24 - 6 a = 1$

Subtract $6 a$ from $11 a$ .

$5 a - 24 = 1$

Step 3

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

Add $24$ to both sides of the equation.

$5 a = 1 + 24$

Add $1$ and $24$ .

$5 a = 25$

Step 4

Divide each term in $5 a = 25$ by $5$ and simplify.

Divide each term in $5 a = 25$ by $5$ .

$\frac{5 a}{5} = \frac{25}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{25}{5}$

Divide $a$ by $1$ .

$a = \frac{25}{5}$

Simplify the right side.

Divide $25$ by $5$ .

$a = 5$