Answer:
x = -3 or x = -2
Step-by-step explanation:
Our equation is: [tex]3x^2+15x+18=0[/tex] .
We see that all three terms are multiples of 3, so let's just divide both sides by 3 to simplify: [tex]\frac{3x^2+15x+18}{3} =\frac{0}{3}[/tex] . We now have: [tex]x^2+5x+6=0[/tex].
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: [tex]x^2+5x+6=(x + 3)(x + 2)=0[/tex].
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!
