Solve by Factoring z^2+z-6=0

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

Step 1

Factor $z^{2} + z - 6$ 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 $1$ .

$- 2, 3$

Write the factored form using these integers.

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

Step 2

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 3

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

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

$z - 2 = 0$

Add $2$ to both sides of the equation.

$z = 2$

Step 4

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 5

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

$z = 2, - 3$

Solve by Factoring z^2+z-6=0

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