Solve for x n*(17+x)=34x-r

$n \cdot (17 + x) = 34 x - r$

Step 1

Simplify $n \cdot (17 + x)$ .

Rewrite.

$0 + 0 + n \cdot (17 + x) = 34 x - r$

Simplify by adding zeros.

$n \cdot (17 + x) = 34 x - r$

Apply the distributive property.

$n \cdot 17 + n x = 34 x - r$

Move $17$ to the left of $n$ .

$17 n + n x = 34 x - r$

Step 2

Subtract $34 x$ from both sides of the equation.

$17 n + n x - 34 x = - r$

Step 3

Subtract $17 n$ from both sides of the equation.

$n x - 34 x = - r - 17 n$

Step 4

Factor $x$ out of $n x - 34 x$ .

Factor $x$ out of $n x$ .

$x n - 34 x = - r - 17 n$

Factor $x$ out of $- 34 x$ .

$x n + x \cdot - 34 = - r - 17 n$

Factor $x$ out of $x n + x \cdot - 34$ .

$x (n - 34) = - r - 17 n$

Step 5

Divide each term in $x (n - 34) = - r - 17 n$ by $n - 34$ and simplify.

Divide each term in $x (n - 34) = - r - 17 n$ by $n - 34$ .

$\frac{x (n - 34)}{n - 34} = \frac{- r}{n - 34} + \frac{- 17 n}{n - 34}$

Simplify the left side.

Cancel the common factor of $n - 34$ .

Cancel the common factor.

$\frac{x (n - 34)}{n - 34} = \frac{- r}{n - 34} + \frac{- 17 n}{n - 34}$

Divide $x$ by $1$ .

$x = \frac{- r}{n - 34} + \frac{- 17 n}{n - 34}$

Simplify the right side.

Combine the numerators over the common denominator.

$x = \frac{- r - 17 n}{n - 34}$

Factor $- 1$ out of $- r$ .

$x = \frac{- (r) - 17 n}{n - 34}$

Factor $- 1$ out of $- 17 n$ .

$x = \frac{- (r) - (17 n)}{n - 34}$

Factor $- 1$ out of $- (r) - (17 n)$ .

$x = \frac{- (r + 17 n)}{n - 34}$

Simplify the expression.

Rewrite $- (r + 17 n)$ as $- 1 (r + 17 n)$ .

$x = \frac{- 1 (r + 17 n)}{n - 34}$

Move the negative in front of the fraction.

$x = - \frac{r + 17 n}{n - 34}$

Solve for x n*(17+x)=34x-r

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