Solve by Factoring (3y+9)^2=81

${(3 y + 9)}^{2} = 81$

Subtract $81$ from both sides of the equation.

${(3 y + 9)}^{2} - 81 = 0$

Simplify ${(3 y + 9)}^{2} - 81$ .

Simplify each term.

Rewrite ${(3 y + 9)}^{2}$ as $(3 y + 9) (3 y + 9)$ .

$(3 y + 9) (3 y + 9) - 81 = 0$

Expand $(3 y + 9) (3 y + 9)$ using the FOIL Method.

Apply the distributive property.

$3 y (3 y + 9) + 9 (3 y + 9) - 81 = 0$

Apply the distributive property.

$3 y (3 y) + 3 y \cdot 9 + 9 (3 y + 9) - 81 = 0$

Apply the distributive property.

$3 y (3 y) + 3 y \cdot 9 + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 y \cdot y + 3 y \cdot 9 + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$3 \cdot 3 (y \cdot y) + 3 y \cdot 9 + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Multiply $y$ by $y$ .

$3 \cdot 3 y^{2} + 3 y \cdot 9 + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Multiply $3$ by $3$ .

$9 y^{2} + 3 y \cdot 9 + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Multiply $9$ by $3$ .

$9 y^{2} + 27 y + 9 (3 y) + 9 \cdot 9 - 81 = 0$

Multiply $3$ by $9$ .

$9 y^{2} + 27 y + 27 y + 9 \cdot 9 - 81 = 0$

Multiply $9$ by $9$ .

$9 y^{2} + 27 y + 27 y + 81 - 81 = 0$

Add $27 y$ and $27 y$ .

$9 y^{2} + 54 y + 81 - 81 = 0$

Combine the opposite terms in $9 y^{2} + 54 y + 81 - 81$ .

Subtract $81$ from $81$ .

$9 y^{2} + 54 y + 0 = 0$

Add $9 y^{2} + 54 y$ and $0$ .

$9 y^{2} + 54 y = 0$

Factor $9 y$ out of $9 y^{2} + 54 y$ .

Factor $9 y$ out of $9 y^{2}$ .

$9 y (y) + 54 y = 0$

Factor $9 y$ out of $54 y$ .

$9 y (y) + 9 y (6) = 0$

Factor $9 y$ out of $9 y (y) + 9 y (6)$ .

$9 y (y + 6) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y = 0$

$y + 6 = 0$

Set $y$ equal to $0$ .

$y = 0$

Set $y + 6$ equal to $0$ and solve for $y$ .

Set $y + 6$ equal to $0$ .

$y + 6 = 0$

Subtract $6$ from both sides of the equation.

$y = - 6$

The final solution is all the values that make $9 y (y + 6) = 0$ true.

$y = 0, - 6$

Solve by Factoring (3y+9)^2=81

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