Find the Roots (Zeros) 3(x+3)^2-81=0

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

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

Simplify each term.

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

$3 ((x + 3) (x + 3)) - 81 = 0$

Expand $(x + 3) (x + 3)$ using the FOIL Method.

Apply the distributive property.

$3 (x (x + 3) + 3 (x + 3)) - 81 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 3 + 3 (x + 3)) - 81 = 0$

Apply the distributive property.

$3 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 81 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

Multiply $3$ by $3$ .

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

Add $3 x$ and $3 x$ .

$3 (x^{2} + 6 x + 9) - 81 = 0$

Apply the distributive property.

$3 x^{2} + 3 (6 x) + 3 \cdot 9 - 81 = 0$

Simplify.

Multiply $6$ by $3$ .

$3 x^{2} + 18 x + 3 \cdot 9 - 81 = 0$

Multiply $3$ by $9$ .

$3 x^{2} + 18 x + 27 - 81 = 0$

Subtract $81$ from $27$ .

$3 x^{2} + 18 x - 54 = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 8.19615242, 2.19615242$