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

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

Step 1

Add $6$ to both sides of the equation.

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

Step 2

Factor the left side of the equation.

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

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

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

Factor $3$ out of $9 x$ .

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

Factor $3$ out of $6$ .

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

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

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

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

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

Factor.

Factor $x^{2} + 3 x + 2$ 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.

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

Remove unnecessary parentheses.

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

Step 3

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

$x + 1 = 0$

$x + 2 = 0$

Step 4

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 5

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

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

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 6

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

$x = - 1, - 2$

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

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