Trigonometry Examples

$- 6 (n + 2) + 13 = - 3 n - 5$

Step 1

Simplify $- 6 (n + 2) + 13$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 6 n - 6 \cdot 2 + 13 = - 3 n - 5$

Step 1.1.2

Multiply $- 6$ by $2$ .

$- 6 n - 12 + 13 = - 3 n - 5$

Step 1.2

Add $- 12$ and $13$ .

$- 6 n + 1 = - 3 n - 5$

Step 2

Move all terms containing $n$ to the left side of the equation.

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Step 2.1

Add $3 n$ to both sides of the equation.

$- 6 n + 1 + 3 n = - 5$

Step 2.2

Add $- 6 n$ and $3 n$ .

$- 3 n + 1 = - 5$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$- 3 n = - 5 - 1$

Step 3.2

Subtract $1$ from $- 5$ .

$- 3 n = - 6$

Step 4

Divide each term in $- 3 n = - 6$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 n = - 6$ by $- 3$ .

$\frac{- 3 n}{- 3} = \frac{- 6}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 n}{- 3} = \frac{- 6}{- 3}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 6}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 6$ by $- 3$ .

$n = 2$