Basic Math Examples

n (n - 1) = 12

$n (n - 1) = 12$

Step 1

Simplify

n (n - 1)

$n (n - 1)$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

n \cdot n + n \cdot - 1 = 12

$n \cdot n + n \cdot - 1 = 12$

Step 1.1.2

Simplify the expression.

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Step 1.1.2.1

Multiply

n

$n$ by

n

$n$ .

n^{2} + n \cdot - 1 = 12

$n^{2} + n \cdot - 1 = 12$

Step 1.1.2.2

Move

- 1

$- 1$ to the left of

n

$n$ .

n^{2} - 1 \cdot n = 12

$n^{2} - 1 \cdot n = 12$

n^{2} - 1 \cdot n = 12

$n^{2} - 1 \cdot n = 12$

n^{2} - 1 \cdot n = 12

$n^{2} - 1 \cdot n = 12$

Step 1.2

Rewrite

- 1 n

$- 1 n$ as

- n

$- n$ .

n^{2} - n = 12

$n^{2} - n = 12$

n^{2} - n = 12

$n^{2} - n = 12$

Step 2

Subtract

12

$12$ from both sides of the equation.

n^{2} - n - 12 = 0

$n^{2} - n - 12 = 0$

Step 3

Factor

n^{2} - n - 12

$n^{2} - n - 12$ using the AC method.

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Step 3.1

Consider the form

x^{2} + b x + c

$x^{2} + b x + c$ . Find a pair of integers whose product is

c

$c$ and whose sum is

b

$b$ . In this case, whose product is

- 12

$- 12$ and whose sum is

- 1

$- 1$ .

- 4, 3

$- 4, 3$

Step 3.2

Write the factored form using these integers.

(n - 4) (n + 3) = 0

$(n - 4) (n + 3) = 0$

(n - 4) (n + 3) = 0

$(n - 4) (n + 3) = 0$

Step 4

If any individual factor on the left side of the equation is equal to

0

$0$ , the entire expression will be equal to

0

$0$ .

n - 4 = 0

$n - 4 = 0$

n + 3 = 0

$n + 3 = 0$

Step 5

Set

n - 4

$n - 4$ equal to

0

$0$ and solve for

n

$n$ .

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Step 5.1

Set

n - 4

$n - 4$ equal to

0

$0$ .

n - 4 = 0

$n - 4 = 0$

Step 5.2

Add

4

$4$ to both sides of the equation.

n = 4

$n = 4$

n = 4

$n = 4$

Step 6

Set

n + 3

$n + 3$ equal to

0

$0$ and solve for

n

$n$ .

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Step 6.1

Set

n + 3

$n + 3$ equal to

0

$0$ .

n + 3 = 0

$n + 3 = 0$

Step 6.2

Subtract

3

$3$ from both sides of the equation.

n = - 3

$n = - 3$

n = - 3

$n = - 3$

Step 7

The final solution is all the values that make

(n - 4) (n + 3) = 0

$(n - 4) (n + 3) = 0$ true.

n = 4, - 3

$n = 4, - 3$

n (n - 1) = 12

$n (n - 1) = 12$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$