Algebra Examples

$p (n) = 52 n - 0.05 n^{2}$

Step 1

Since $n$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$52 n - 0.05 n^{2} = p n$

Step 2

Subtract $p n$ from both sides of the equation.

$52 n - 0.05 n^{2} - p n = 0$

Step 3

Factor $0.05 n$ out of $52 n - 0.05 n^{2} - p n$ .

Tap for more steps...

Step 3.1

Move $p$ .

$52 n - 0.05 n^{2} - 1 n p = 0$

Step 3.2

Factor $0.05 n$ out of $52 n$ .

$0.05 n (1040) - 0.05 n^{2} - 1 n p = 0$

Step 3.3

Factor $0.05 n$ out of $- 0.05 n^{2}$ .

$0.05 n (1040) + 0.05 n (- n) - 1 n p = 0$

Step 3.4

Factor $0.05 n$ out of $- 1 n p$ .

$0.05 n (1040) + 0.05 n (- n) + 0.05 n (- 20 p) = 0$

Step 3.5

Factor $0.05 n$ out of $0.05 n (1040) + 0.05 n (- n)$ .

$0.05 n (1040 - n) + 0.05 n (- 20 p) = 0$

Step 3.6

Factor $0.05 n$ out of $0.05 n (1040 - n) + 0.05 n (- 20 p)$ .

$0.05 n (1040 - n - 20 p) = 0$

Step 4

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

$n = 0$

$1040 - n - 20 p = 0$

Step 5

Set $n$ equal to $0$ .

$n = 0$

Step 6

Set $1040 - n - 20 p$ equal to $0$ and solve for $n$ .

Tap for more steps...

Step 6.1

Set $1040 - n - 20 p$ equal to $0$ .

$1040 - n - 20 p = 0$

Step 6.2

Solve $1040 - n - 20 p = 0$ for $n$ .

Tap for more steps...

Step 6.2.1

Move all terms not containing $n$ to the right side of the equation.

Tap for more steps...

Step 6.2.1.1

Subtract $1040$ from both sides of the equation.

$- n - 20 p = - 1040$

Step 6.2.1.2

Add $20 p$ to both sides of the equation.

$- n = - 1040 + 20 p$

Step 6.2.2

Divide each term in $- n = - 1040 + 20 p$ by $- 1$ and simplify.

Tap for more steps...

Step 6.2.2.1

Divide each term in $- n = - 1040 + 20 p$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- 1040}{- 1} + \frac{20 p}{- 1}$

Step 6.2.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- 1040}{- 1} + \frac{20 p}{- 1}$

Step 6.2.2.2.2

Divide $n$ by $1$ .

$n = \frac{- 1040}{- 1} + \frac{20 p}{- 1}$

Step 6.2.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.2.3.1

Simplify each term.

Tap for more steps...

Step 6.2.2.3.1.1

Divide $- 1040$ by $- 1$ .

$n = 1040 + \frac{20 p}{- 1}$

Step 6.2.2.3.1.2

Move the negative one from the denominator of $\frac{20 p}{- 1}$ .

$n = 1040 - 1 \cdot (20 p)$

Step 6.2.2.3.1.3

Rewrite $- 1 \cdot (20 p)$ as $- (20 p)$ .

$n = 1040 - (20 p)$

Step 6.2.2.3.1.4

Multiply $20$ by $- 1$ .

$n = 1040 - 20 p$

Step 7

The final solution is all the values that make $0.05 n (1040 - n - 20 p) = 0$ true.

$n = 0$

$n = 1040 - 20 p$