Solve for d 10-3(2d-9)+d=9(d+1)

$10 - 3 (2 d - 9) + d = 9 (d + 1)$

Step 1

Simplify $10 - 3 (2 d - 9) + d$ .

Simplify each term.

Apply the distributive property.

$10 - 3 (2 d) - 3 \cdot - 9 + d = 9 (d + 1)$

Multiply $2$ by $- 3$ .

$10 - 6 d - 3 \cdot - 9 + d = 9 (d + 1)$

Multiply $- 3$ by $- 9$ .

$10 - 6 d + 27 + d = 9 (d + 1)$

Simplify by adding terms.

Add $10$ and $27$ .

$- 6 d + 37 + d = 9 (d + 1)$

Add $- 6 d$ and $d$ .

$- 5 d + 37 = 9 (d + 1)$

Step 2

Simplify $9 (d + 1)$ .

Apply the distributive property.

$- 5 d + 37 = 9 d + 9 \cdot 1$

Multiply $9$ by $1$ .

$- 5 d + 37 = 9 d + 9$

Step 3

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

Subtract $9 d$ from both sides of the equation.

$- 5 d + 37 - 9 d = 9$

Subtract $9 d$ from $- 5 d$ .

$- 14 d + 37 = 9$

Step 4

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

Subtract $37$ from both sides of the equation.

$- 14 d = 9 - 37$

Subtract $37$ from $9$ .

$- 14 d = - 28$

Step 5

Divide each term in $- 14 d = - 28$ by $- 14$ and simplify.

Divide each term in $- 14 d = - 28$ by $- 14$ .

$\frac{- 14 d}{- 14} = \frac{- 28}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 d}{- 14} = \frac{- 28}{- 14}$

Divide $d$ by $1$ .

$d = \frac{- 28}{- 14}$

Simplify the right side.

Divide $- 28$ by $- 14$ .

$d = 2$