Solve for q 18q-2q^2=0

$18 q - 2 q^{2} = 0$

Step 1

Factor the left side of the equation.

Let $u = q$ . Substitute $u$ for all occurrences of $q$ .

$18 u - 2 u^{2} = 0$

Factor $2 u$ out of $18 u - 2 u^{2}$ .

Factor $2 u$ out of $18 u$ .

$2 u (9) - 2 u^{2} = 0$

Factor $2 u$ out of $- 2 u^{2}$ .

$2 u (9) + 2 u (- u) = 0$

Factor $2 u$ out of $2 u (9) + 2 u (- u)$ .

$2 u (9 - u) = 0$

Replace all occurrences of $u$ with $q$ .

$2 q (9 - q) = 0$

Step 2

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

$q = 0$

$9 - q = 0$

Step 3

Set $q$ equal to $0$ .

$q = 0$

Step 4

Set $9 - q$ equal to $0$ and solve for $q$ .

Set $9 - q$ equal to $0$ .

$9 - q = 0$

Solve $9 - q = 0$ for $q$ .

Subtract $9$ from both sides of the equation.

$- q = - 9$

Divide each term in $- q = - 9$ by $- 1$ and simplify.

Divide each term in $- q = - 9$ by $- 1$ .

$\frac{- q}{- 1} = \frac{- 9}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{q}{1} = \frac{- 9}{- 1}$

Divide $q$ by $1$ .

$q = \frac{- 9}{- 1}$

Simplify the right side.

Divide $- 9$ by $- 1$ .

$q = 9$

Step 5

The final solution is all the values that make $2 q (9 - q) = 0$ true.

$q = 0, 9$