Solve for p 3p^2+9p=-6

$3 p^{2} + 9 p = - 6$

Add $6$ to both sides of the equation.

$3 p^{2} + 9 p + 6 = 0$

Factor the left side of the equation.

Factor $3$ out of $3 p^{2} + 9 p + 6$ .

Factor $3$ out of $3 p^{2}$ .

$3 (p^{2}) + 9 p + 6 = 0$

Factor $3$ out of $9 p$ .

$3 (p^{2}) + 3 (3 p) + 6 = 0$

Factor $3$ out of $6$ .

$3 p^{2} + 3 (3 p) + 3 \cdot 2 = 0$

Factor $3$ out of $3 p^{2} + 3 (3 p)$ .

$3 (p^{2} + 3 p) + 3 \cdot 2 = 0$

Factor $3$ out of $3 (p^{2} + 3 p) + 3 \cdot 2$ .

$3 (p^{2} + 3 p + 2) = 0$

Factor.

Factor $p^{2} + 3 p + 2$ 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 $2$ and whose sum is $3$ .

$1, 2$

Write the factored form using these integers.

$3 ((p + 1) (p + 2)) = 0$

Remove unnecessary parentheses.

$3 (p + 1) (p + 2) = 0$

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

$p + 1 = 0$

$p + 2 = 0$

Set $p + 1$ equal to $0$ and solve for $p$ .

Set $p + 1$ equal to $0$ .

$p + 1 = 0$

Subtract $1$ from both sides of the equation.

$p = - 1$

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

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

$p + 2 = 0$

Subtract $2$ from both sides of the equation.

$p = - 2$

The final solution is all the values that make $3 (p + 1) (p + 2) = 0$ true.

$p = - 1, - 2$

Solve for p 3p^2+9p=-6

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