Solve by Factoring z^2+5z=-6

$z^{2} + 5 z = - 6$

Step 1

Add $6$ to both sides of the equation.

$z^{2} + 5 z + 6 = 0$

Step 2

Factor $z^{2} + 5 z + 6$ 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 $6$ and whose sum is $5$ .

$2, 3$

Write the factored form using these integers.

$(z + 2) (z + 3) = 0$

Step 3

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

$z + 2 = 0$

$z + 3 = 0$

Step 4

Set $z + 2$ equal to $0$ and solve for $z$ .

Set $z + 2$ equal to $0$ .

$z + 2 = 0$

Subtract $2$ from both sides of the equation.

$z = - 2$

Step 5

Set $z + 3$ equal to $0$ and solve for $z$ .

Set $z + 3$ equal to $0$ .

$z + 3 = 0$

Subtract $3$ from both sides of the equation.

$z = - 3$

Step 6

The final solution is all the values that make $(z + 2) (z + 3) = 0$ true.

$z = - 2, - 3$

Solve by Factoring z^2+5z=-6

Related Questions

Support LCMGCF.com by disabling your adblocker.