Solve for n 8=-18+3/8(16-40n)

$8 = - 18 + \frac{3}{8} (16 - 40 n)$

Step 1

Rewrite the equation as $- 18 + \frac{3}{8} \cdot (16 - 40 n) = 8$ .

$- 18 + \frac{3}{8} \cdot (16 - 40 n) = 8$

Step 2

Simplify $- 18 + \frac{3}{8} \cdot (16 - 40 n)$ .

Simplify each term.

Apply the distributive property.

$- 18 + \frac{3}{8} \cdot 16 + \frac{3}{8} (- 40 n) = 8$

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$- 18 + \frac{3}{8} \cdot (8 (2)) + \frac{3}{8} (- 40 n) = 8$

Cancel the common factor.

$- 18 + \frac{3}{8} \cdot (8 \cdot 2) + \frac{3}{8} (- 40 n) = 8$

Rewrite the expression.

$- 18 + 3 \cdot 2 + \frac{3}{8} (- 40 n) = 8$

Multiply $3$ by $2$ .

$- 18 + 6 + \frac{3}{8} (- 40 n) = 8$

Cancel the common factor of $8$ .

Factor $8$ out of $- 40 n$ .

$- 18 + 6 + \frac{3}{8} (8 (- 5 n)) = 8$

Cancel the common factor.

$- 18 + 6 + \frac{3}{8} (8 (- 5 n)) = 8$

Rewrite the expression.

$- 18 + 6 + 3 (- 5 n) = 8$

Multiply $- 5$ by $3$ .

$- 18 + 6 - 15 n = 8$

Add $- 18$ and $6$ .

$- 12 - 15 n = 8$

Step 3

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

Add $12$ to both sides of the equation.

$- 15 n = 8 + 12$

Add $8$ and $12$ .

$- 15 n = 20$

Step 4

Divide each term in $- 15 n = 20$ by $- 15$ and simplify.

Divide each term in $- 15 n = 20$ by $- 15$ .

$\frac{- 15 n}{- 15} = \frac{20}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 n}{- 15} = \frac{20}{- 15}$

Divide $n$ by $1$ .

$n = \frac{20}{- 15}$

Simplify the right side.

Cancel the common factor of $20$ and $- 15$ .

Factor $5$ out of $20$ .

$n = \frac{5 (4)}{- 15}$

Cancel the common factors.

Factor $5$ out of $- 15$ .

$n = \frac{5 \cdot 4}{5 \cdot - 3}$

Cancel the common factor.

$n = \frac{5 \cdot 4}{5 \cdot - 3}$

Rewrite the expression.

$n = \frac{4}{- 3}$

Move the negative in front of the fraction.

$n = - \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{4}{3}$

Decimal Form:

$n = - 1.\overline{3}$

Mixed Number Form:

$n = - 1 \frac{1}{3}$

Solve for n 8=-18+3/8(16-40n)

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