Basic Math Examples

$\frac{(n + 4) (n + 4 - 9)}{2} = 26$

Step 1

Multiply both sides of the equation by $2$ .

$2 \frac{(n + 4) (n + 4 - 9)}{2} = 2 \cdot 26$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 \frac{(n + 4) (n + 4 - 9)}{2}$ .

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Step 2.1.1.1

Reduce the expression by cancelling the common factors.

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Step 2.1.1.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1.1.1

Cancel the common factor.

$2 \frac{(n + 4) (n + 4 - 9)}{2} = 2 \cdot 26$

Step 2.1.1.1.1.2

Rewrite the expression.

$(n + 4) (n + 4 - 9) = 2 \cdot 26$

Step 2.1.1.1.2

Subtract $9$ from $4$ .

$(n + 4) (n - 5) = 2 \cdot 26$

Step 2.1.1.2

Expand $(n + 4) (n - 5)$ using the FOIL Method.

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Step 2.1.1.2.1

Apply the distributive property.

$n (n - 5) + 4 (n - 5) = 2 \cdot 26$

Step 2.1.1.2.2

Apply the distributive property.

$n \cdot n + n \cdot - 5 + 4 (n - 5) = 2 \cdot 26$

Step 2.1.1.2.3

Apply the distributive property.

$n \cdot n + n \cdot - 5 + 4 n + 4 \cdot - 5 = 2 \cdot 26$

Step 2.1.1.3

Simplify and combine like terms.

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Step 2.1.1.3.1

Simplify each term.

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Step 2.1.1.3.1.1

Multiply $n$ by $n$ .

$n^{2} + n \cdot - 5 + 4 n + 4 \cdot - 5 = 2 \cdot 26$

Step 2.1.1.3.1.2

Move $- 5$ to the left of $n$ .

$n^{2} - 5 \cdot n + 4 n + 4 \cdot - 5 = 2 \cdot 26$

Step 2.1.1.3.1.3

Multiply $4$ by $- 5$ .

$n^{2} - 5 n + 4 n - 20 = 2 \cdot 26$

Step 2.1.1.3.2

Add $- 5 n$ and $4 n$ .

$n^{2} - n - 20 = 2 \cdot 26$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $26$ .

$n^{2} - n - 20 = 52$

Step 3

Subtract $52$ from both sides of the equation.

$n^{2} - n - 20 - 52 = 0$

Step 4

Subtract $52$ from $- 20$ .

$n^{2} - n - 72 = 0$

Step 5

Factor $n^{2} - n - 72$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Step 5.2

Write the factored form using these integers.

$(n - 9) (n + 8) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$n - 9 = 0$

$n + 8 = 0$

Step 7

Set $n - 9$ equal to $0$ and solve for $n$ .

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Step 7.1

Set $n - 9$ equal to $0$ .

$n - 9 = 0$

Step 7.2

Add $9$ to both sides of the equation.

$n = 9$

Step 8

Set $n + 8$ equal to $0$ and solve for $n$ .

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Step 8.1

Set $n + 8$ equal to $0$ .

$n + 8 = 0$

Step 8.2

Subtract $8$ from both sides of the equation.

$n = - 8$

Step 9

The final solution is all the values that make $(n - 9) (n + 8) = 0$ true.

$n = 9, - 8$