Question

Solve by factoring.
3x^2+15x+18=0
Show work please :)

Answer 1

x = -3, -2

Explanation:

3x² + 15x + 18 = 0

3(x² + 5x + 6) = 0

x² + 3x + 2x + 6 = 0

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

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

x = -3, -2

Answer 2

x = -3 or x = -2

Explanation:

Our equation is:
`3x^2+15x+18=0` .

We see that all three terms are multiples of 3, so let's just divide both sides by 3 to simplify:
`(3x^2+15x+18)/(3) =(0)/(3)` . We now have:
`x^2+5x+6=0`.

To factor this, we want to look at the pairs of factors of the constant 6 and see which pair will add up to 5 (from the 5x). After some searching, we can easily see that 3 * 2 = 6 and 3 + 2 = 5, so this is the pair we're looking for. Then, we factor:
`x^2+5x+6=(x + 3)(x + 2)=0`.

Finally, to solve, we know that if x + 3 = 0 or if x + 2 = 0, then the product will be 0, so: x + 3 = 0 --> x = -3 OR x + 2 = 0 --> x = -2

Thus, the answer is: x = -3 or x = -2.

Hope this helps!