Basic Math Examples

$(8 (n + 1) - 5) = 4 \cdot (n + 1^{2}) - (n + 1)$

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.

$4 \cdot (n + 1^{2}) - (n + 1) = 8 (n + 1) - 5$

Step 2

Simplify $4 \cdot (n + 1^{2}) - (n + 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

One to any power is one.

$4 \cdot (n + 1) - (n + 1) = 8 (n + 1) - 5$

Step 2.1.2

Apply the distributive property.

$4 n + 4 \cdot 1 - (n + 1) = 8 (n + 1) - 5$

Step 2.1.3

Multiply $4$ by $1$ .

$4 n + 4 - (n + 1) = 8 (n + 1) - 5$

Step 2.1.4

Apply the distributive property.

$4 n + 4 - n - 1 \cdot 1 = 8 (n + 1) - 5$

Step 2.1.5

Multiply $- 1$ by $1$ .

$4 n + 4 - n - 1 = 8 (n + 1) - 5$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $n$ from $4 n$ .

$3 n + 4 - 1 = 8 (n + 1) - 5$

Step 2.2.2

Subtract $1$ from $4$ .

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

Step 3

Simplify $8 (n + 1) - 5$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$3 n + 3 = 8 n + 8 \cdot 1 - 5$

Step 3.1.2

Multiply $8$ by $1$ .

$3 n + 3 = 8 n + 8 - 5$

Step 3.2

Subtract $5$ from $8$ .

$3 n + 3 = 8 n + 3$

Step 4

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

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Step 4.1

Subtract $8 n$ from both sides of the equation.

$3 n + 3 - 8 n = 3$

Step 4.2

Subtract $8 n$ from $3 n$ .

$- 5 n + 3 = 3$

Step 5

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

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Step 5.1

Subtract $3$ from both sides of the equation.

$- 5 n = 3 - 3$

Step 5.2

Subtract $3$ from $3$ .

$- 5 n = 0$

Step 6

Divide each term in $- 5 n = 0$ by $- 5$ and simplify.

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Step 6.1

Divide each term in $- 5 n = 0$ by $- 5$ .

$\frac{- 5 n}{- 5} = \frac{0}{- 5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 5 n}{- 5} = \frac{0}{- 5}$

Step 6.2.1.2

Divide $n$ by $1$ .

$n = \frac{0}{- 5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $0$ by $- 5$ .

$n = 0$