Find the Roots (Zeros) P(c)=-20(c-3)^2+180

$P (c) = - 20 {(c - 3)}^{2} + 180$

Step 1

Set $- 20 {(c - 3)}^{2} + 180$ equal to $0$ .

$- 20 {(c - 3)}^{2} + 180 = 0$

Step 2

Solve for $x$ .

Simplify $- 20 {(c - 3)}^{2} + 180$ .

Simplify each term.

Rewrite ${(c - 3)}^{2}$ as $(c - 3) (c - 3)$ .

$- 20 ((c - 3) (c - 3)) + 180 = 0$

Expand $(c - 3) (c - 3)$ using the FOIL Method.

Apply the distributive property.

$- 20 (c (c - 3) - 3 (c - 3)) + 180 = 0$

Apply the distributive property.

$- 20 (c \cdot c + c \cdot - 3 - 3 (c - 3)) + 180 = 0$

Apply the distributive property.

$- 20 (c \cdot c + c \cdot - 3 - 3 c - 3 \cdot - 3) + 180 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $c$ by $c$ .

$- 20 (c^{2} + c \cdot - 3 - 3 c - 3 \cdot - 3) + 180 = 0$

Move $- 3$ to the left of $c$ .

$- 20 (c^{2} - 3 \cdot c - 3 c - 3 \cdot - 3) + 180 = 0$

Multiply $- 3$ by $- 3$ .

$- 20 (c^{2} - 3 c - 3 c + 9) + 180 = 0$

Subtract $3 c$ from $- 3 c$ .

$- 20 (c^{2} - 6 c + 9) + 180 = 0$

Apply the distributive property.

$- 20 c^{2} - 20 (- 6 c) - 20 \cdot 9 + 180 = 0$

Simplify.

Multiply $- 6$ by $- 20$ .

$- 20 c^{2} + 120 c - 20 \cdot 9 + 180 = 0$

Multiply $- 20$ by $9$ .

$- 20 c^{2} + 120 c - 180 + 180 = 0$

Combine the opposite terms in $- 20 c^{2} + 120 c - 180 + 180$ .

Add $- 180$ and $180$ .

$- 20 c^{2} + 120 c + 0 = 0$

Add $- 20 c^{2} + 120 c$ and $0$ .

$- 20 c^{2} + 120 c = 0$

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

$c = 0, 6$

Step 3