Algebra Examples

$12 (- 4 + 6 n) = 13 n + 23 (n + 9)$

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.

$13 n + 23 (n + 9) = 12 (- 4 + 6 n)$

Step 2

Simplify $13 n + 23 (n + 9)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$13 n + 23 n + 23 \cdot 9 = 12 (- 4 + 6 n)$

Step 2.1.2

Multiply $23$ by $9$ .

$13 n + 23 n + 207 = 12 (- 4 + 6 n)$

Step 2.2

Add $13 n$ and $23 n$ .

$36 n + 207 = 12 (- 4 + 6 n)$

Step 3

Simplify $12 (- 4 + 6 n)$ .

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Step 3.1

Apply the distributive property.

$36 n + 207 = 12 \cdot - 4 + 12 (6 n)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $12$ by $- 4$ .

$36 n + 207 = - 48 + 12 (6 n)$

Step 3.2.2

Multiply $6$ by $12$ .

$36 n + 207 = - 48 + 72 n$

Step 4

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

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Step 4.1

Subtract $72 n$ from both sides of the equation.

$36 n + 207 - 72 n = - 48$

Step 4.2

Subtract $72 n$ from $36 n$ .

$- 36 n + 207 = - 48$

Step 5

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

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Step 5.1

Subtract $207$ from both sides of the equation.

$- 36 n = - 48 - 207$

Step 5.2

Subtract $207$ from $- 48$ .

$- 36 n = - 255$

Step 6

Divide each term in $- 36 n = - 255$ by $- 36$ and simplify.

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Step 6.1

Divide each term in $- 36 n = - 255$ by $- 36$ .

$\frac{- 36 n}{- 36} = \frac{- 255}{- 36}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 36$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 36 n}{- 36} = \frac{- 255}{- 36}$

Step 6.2.1.2

Divide $n$ by $1$ .

$n = \frac{- 255}{- 36}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Cancel the common factor of $- 255$ and $- 36$ .

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Step 6.3.1.1

Factor $- 3$ out of $- 255$ .

$n = \frac{- 3 (85)}{- 36}$

Step 6.3.1.2

Cancel the common factors.

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Step 6.3.1.2.1

Factor $- 3$ out of $- 36$ .

$n = \frac{- 3 \cdot 85}{- 3 \cdot 12}$

Step 6.3.1.2.2

Cancel the common factor.

$n = \frac{- 3 \cdot 85}{- 3 \cdot 12}$

Step 6.3.1.2.3

Rewrite the expression.

$n = \frac{85}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = \frac{85}{12}$

Decimal Form:

$n = 7.08\overline{3}$

Mixed Number Form:

$n = 7 \frac{1}{12}$