Solve for d d(d+3)-d(d-4)=9d-16

$d (d + 3) - d (d - 4) = 9 d - 16$

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

Simplify each term.

Apply the distributive property.

$d \cdot d + d \cdot 3 - d (d - 4) = 9 d - 16$

Multiply $d$ by $d$ .

$d^{2} + d \cdot 3 - d (d - 4) = 9 d - 16$

Move $3$ to the left of $d$ .

$d^{2} + 3 \cdot d - d (d - 4) = 9 d - 16$

Apply the distributive property.

$d^{2} + 3 d - d \cdot d - d \cdot - 4 = 9 d - 16$

Multiply $d$ by $d$ by adding the exponents.

Move $d$ .

$d^{2} + 3 d - (d \cdot d) - d \cdot - 4 = 9 d - 16$

Multiply $d$ by $d$ .

$d^{2} + 3 d - d^{2} - d \cdot - 4 = 9 d - 16$

Multiply $- 4$ by $- 1$ .

$d^{2} + 3 d - d^{2} + 4 d = 9 d - 16$

Simplify by adding terms.

Combine the opposite terms in $d^{2} + 3 d - d^{2} + 4 d$ .

Subtract $d^{2}$ from $d^{2}$ .

$3 d + 0 + 4 d = 9 d - 16$

Add $3 d$ and $0$ .

$3 d + 4 d = 9 d - 16$

Add $3 d$ and $4 d$ .

$7 d = 9 d - 16$

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

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

$7 d - 9 d = - 16$

Subtract $9 d$ from $7 d$ .

$- 2 d = - 16$

Divide each term in $- 2 d = - 16$ by $- 2$ and simplify.

Divide each term in $- 2 d = - 16$ by $- 2$ .

$\frac{- 2 d}{- 2} = \frac{- 16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 d}{- 2} = \frac{- 16}{- 2}$

Divide $d$ by $1$ .

$d = \frac{- 16}{- 2}$

Simplify the right side.

Divide $- 16$ by $- 2$ .

$d = 8$