How to factor 10k^2+35k+15 completely?

I would start with the easy: factor five out.

5(5k^2 +7x +3)
Now the three tells you that the factors are probably 3,1 and the five tells you that the factors are probably 5,1
5(5k+3)(k+1) wrong, wont work
and 5(5k+1)(k+3) wont work. So the easy is out. Next, the quadratic equation...

k= -b +- sqrt (b^2 -4ac) /2a

k= -7 +- sqrt (49 - 60) /10

Notice the serd: it is negative, so the factors are in the the imaginary plane. You cannot factor the problem in the real number system.

To factor the expression 10k^2 + 35k + 15 completely, you can follow these steps:

1. Check for any common factors: In this case, there are no common factors among the coefficients.

2. Use the quadratic formula: The quadratic formula is a formula that gives you the solutions to an equation in the form ax^2 + bx + c = 0, where a, b, and c are coefficients. In this case, your equation is 10k^2 + 35k + 15 = 0.

The quadratic formula is:
k = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values from your equation, you get:
k = (-35 ± √(35^2 - 4 * 10 * 15)) / (2 * 10)

Simplify this to get two possible values for k: k ≈ -0.5 and k ≈ -3.

3. Write the factored form: Since the quadratic equation has no real roots (the solutions are in the imaginary plane), you cannot factor it in the real number system. Therefore, the factored form remains as 10k^2 + 35k + 15.

In conclusion, the expression 10k^2 + 35k + 15 cannot be factored completely in the real number system.

Note: If you have made a typo in the expression and meant to ask about a different equation, please provide the correct equation so that I can assist you further.