Hello, How can I factor this: 3x^2+16x+5 I tried several times, but still no solution! Thank you?

Have you tried a calculator?

Look at the product of the first and last coefficients.
.. 3*5 = 15
Now, look for factors of 15 that add to 16. It doesn't take many trials.
.. 15 = 1*15 = 3*5
You can see that 1 and 15 add to 16. Now, rewrite the middle term as a sum using these numbers.
.. 3x^2 + 1x + 15x + 5
Now factor pairwise.
.. x(3x+1) + 5(3x+1)
Now, factor out the common factor.
.. (x+5)(3x+1) ... completed factoring

First, let's see if it can be factored.

For it to be factorable, it needs to have rational roots. To test for rational roots, check the discriminant to see if it's a positive square number.

b² - 4ac
16² - 4(3)(5)
256 - 60
196

That is a square number, so it can factor.

If you are like me and can't see the factors if the coefficient of x² is more than 1, then find the roots and turn them into factors:

x = [ -b ± √(b² - 4ac)] / (2a)

We already know what the discriminant is, so just substitute that and simplify:

x = [ -16 ± √(196)] / (2*3)
x = (-16 ± 14) / 6
x = -30/6 and -2/6
x = -5 and -1/3

So this would factor to:

(3x + 1)(x + 5)

3x²+16x+5

3(5) = 15
find factors of 15 that add to 16
try 15 and 1

change 16x to 15x + x

3x² + 15x + x + 5
3x(x+5) + 1(x+5)
(3x+1)(x+5)

Or
3x²+16x+5
factor 3x² into 3x and x
factor 5 into 5 and 1

try factor pairs and FOIL to check
(3x+5)(x+1) no
(3x+1)(x+5) yes