Solve for y y^2+5y=36

$y^{2} + 5 y = 36$

Step 1

Subtract $36$ from both sides of the equation.

$y^{2} + 5 y - 36 = 0$

Step 2

Factor $y^{2} + 5 y - 36$ 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 $- 36$ and whose sum is $5$ .

$- 4, 9$

Write the factored form using these integers.

$(y - 4) (y + 9) = 0$

Step 3

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

$y - 4 = 0$

$y + 9 = 0$

Step 4

Set $y - 4$ equal to $0$ and solve for $y$ .

Set $y - 4$ equal to $0$ .

$y - 4 = 0$

Add $4$ to both sides of the equation.

$y = 4$

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 $(y - 4) (y + 9) = 0$ true.

$y = 4, - 9$

Solve for y y^2+5y=36

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