Basic Math Examples

$5 (3 n + 1) = 2 (5 n - 4) + 6 n$

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.

$2 (5 n - 4) + 6 n = 5 (3 n + 1)$

Step 2

Simplify $2 (5 n - 4) + 6 n$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$2 (5 n) + 2 \cdot - 4 + 6 n = 5 (3 n + 1)$

Step 2.1.2

Multiply $5$ by $2$ .

$10 n + 2 \cdot - 4 + 6 n = 5 (3 n + 1)$

Step 2.1.3

Multiply $2$ by $- 4$ .

$10 n - 8 + 6 n = 5 (3 n + 1)$

Step 2.2

Add $10 n$ and $6 n$ .

$16 n - 8 = 5 (3 n + 1)$

Step 3

Simplify $5 (3 n + 1)$ .

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Step 3.1

Apply the distributive property.

$16 n - 8 = 5 (3 n) + 5 \cdot 1$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $3$ by $5$ .

$16 n - 8 = 15 n + 5 \cdot 1$

Step 3.2.2

Multiply $5$ by $1$ .

$16 n - 8 = 15 n + 5$

Step 4

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

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Step 4.1

Subtract $15 n$ from both sides of the equation.

$16 n - 8 - 15 n = 5$

Step 4.2

Subtract $15 n$ from $16 n$ .

$n - 8 = 5$

Step 5

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

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Step 5.1

Add $8$ to both sides of the equation.

$n = 5 + 8$

Step 5.2

Add $5$ and $8$ .

$n = 13$