Solve for x 3x^2+18x+13=-2

$3 x^{2} + 18 x + 13 = - 2$

Step 1

Add $2$ to both sides of the equation.

$3 x^{2} + 18 x + 13 + 2 = 0$

Step 2

Add $13$ and $2$ .

$3 x^{2} + 18 x + 15 = 0$

Step 3

Factor the left side of the equation.

Factor $3$ out of $3 x^{2} + 18 x + 15$ .

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

$3 (x^{2}) + 18 x + 15 = 0$

Factor $3$ out of $18 x$ .

$3 (x^{2}) + 3 (6 x) + 15 = 0$

Factor $3$ out of $15$ .

$3 x^{2} + 3 (6 x) + 3 \cdot 5 = 0$

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

$3 (x^{2} + 6 x) + 3 \cdot 5 = 0$

Factor $3$ out of $3 (x^{2} + 6 x) + 3 \cdot 5$ .

$3 (x^{2} + 6 x + 5) = 0$

Factor.

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

$1, 5$

Write the factored form using these integers.

$3 ((x + 1) (x + 5)) = 0$

Remove unnecessary parentheses.

$3 (x + 1) (x + 5) = 0$

Step 4

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

$x + 1 = 0$

$x + 5 = 0$

Step 5

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 6

Set $x + 5$ equal to $0$ and solve for $x$ .

Set $x + 5$ equal to $0$ .

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 7

The final solution is all the values that make $3 (x + 1) (x + 5) = 0$ true.

$x = - 1, - 5$

Solve for x 3x^2+18x+13=-2

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