Solve for d 3(4d+1)-9d=6(2-d)

$3 (4 d + 1) - 9 d = 6 (2 - d)$

Step 1

Simplify $3 (4 d + 1) - 9 d$ .

Simplify each term.

Apply the distributive property.

$3 (4 d) + 3 \cdot 1 - 9 d = 6 (2 - d)$

Multiply $4$ by $3$ .

$12 d + 3 \cdot 1 - 9 d = 6 (2 - d)$

Multiply $3$ by $1$ .

$12 d + 3 - 9 d = 6 (2 - d)$

Subtract $9 d$ from $12 d$ .

$3 d + 3 = 6 (2 - d)$

Step 2

Simplify $6 (2 - d)$ .

Apply the distributive property.

$3 d + 3 = 6 \cdot 2 + 6 (- d)$

Multiply.

Multiply $6$ by $2$ .

$3 d + 3 = 12 + 6 (- d)$

Multiply $- 1$ by $6$ .

$3 d + 3 = 12 - 6 d$

Step 3

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

Add $6 d$ to both sides of the equation.

$3 d + 3 + 6 d = 12$

Add $3 d$ and $6 d$ .

$9 d + 3 = 12$

Step 4

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

Subtract $3$ from both sides of the equation.

$9 d = 12 - 3$

Subtract $3$ from $12$ .

$9 d = 9$

Step 5

Divide each term in $9 d = 9$ by $9$ and simplify.

Divide each term in $9 d = 9$ by $9$ .

$\frac{9 d}{9} = \frac{9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 d}{9} = \frac{9}{9}$

Divide $d$ by $1$ .

$d = \frac{9}{9}$

Simplify the right side.

Divide $9$ by $9$ .

$d = 1$

Solve for d 3(4d+1)-9d=6(2-d)

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