Basic Math Examples

y^{2} - y = 6

$y^{2} - y = 6$

Step 1

Subtract

6

$6$ from both sides of the equation.

y^{2} - y - 6 = 0

$y^{2} - y - 6 = 0$

Step 2

Factor

y^{2} - y - 6

$y^{2} - y - 6$ using the AC method.

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Step 2.1

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

- 6

$- 6$ and whose sum is

- 1

$- 1$ .

- 3, 2

$- 3, 2$

Step 2.2

Write the factored form using these integers.

(y - 3) (y + 2) = 0

$(y - 3) (y + 2) = 0$

(y - 3) (y + 2) = 0

$(y - 3) (y + 2) = 0$

Step 3

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

0

$0$ , the entire expression will be equal to

0

$0$ .

y - 3 = 0

$y - 3 = 0$

y + 2 = 0

$y + 2 = 0$

Step 4

Set

y - 3

$y - 3$ equal to

0

$0$ and solve for

y

$y$ .

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Step 4.1

Set

y - 3

$y - 3$ equal to

0

$0$ .

y - 3 = 0

$y - 3 = 0$

Step 4.2

Add

3

$3$ to both sides of the equation.

y = 3

$y = 3$

y = 3

$y = 3$

Step 5

Set

y + 2

$y + 2$ equal to

0

$0$ and solve for

y

$y$ .

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Step 5.1

Set

y + 2

$y + 2$ equal to

0

$0$ .

y + 2 = 0

$y + 2 = 0$

Step 5.2

Subtract

2

$2$ from both sides of the equation.

y = - 2

$y = - 2$

y = - 2

$y = - 2$

Step 6

The final solution is all the values that make

(y - 3) (y + 2) = 0

$(y - 3) (y + 2) = 0$ true.

y = 3, - 2

$y = 3, - 2$