Solve by Factoring y^2+7y=18

$y^{2} + 7 y = 18$

Step 1

Subtract $18$ from both sides of the equation.

$y^{2} + 7 y - 18 = 0$

Step 2

Factor $y^{2} + 7 y - 18$ using the AC method.

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 $- 18$ and whose sum is $7$ .

$- 2, 9$

Write the factored form using these integers.

$(y - 2) (y + 9) = 0$

Step 3

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

$y - 2 = 0$

$y + 9 = 0$

Step 4

Set $y - 2$ equal to $0$ and solve for $y$ .

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

Add $2$ to both sides of the equation.

$y = 2$

Step 5

Set $y + 9$ equal to $0$ and solve for $y$ .

Set $y + 9$ equal to $0$ .

$y + 9 = 0$

Subtract $9$ from both sides of the equation.

$y = - 9$

Step 6

The final solution is all the values that make $(y - 2) (y + 9) = 0$ true.

$y = 2, - 9$

Solve by Factoring y^2+7y=18

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