Question

Explain Step By Step How to Solve the Following Equation by Factoring: 3n^2+14n+15

Answer 1

The expression 3n^2 can be separated into (3n)(n).

Factored formula is in the form (a+b)(a+b), where b*b is equal to the last term in the expression, 15. The factors of 15 are three and five.

Using these two piece of information, we know it must be either (3n+3)(n+5) or (3n+5)(n+3). To get the middle term, 14n, using FOIL, this is equivalent to ((3n)(3) + (5)(n)) in the latter expression. In the first expression, ((3n)(5) + (3)(n)) = 18n, which is not equivalent to the given equation’s middle term.

Therefore, we know that the factored form of this equation is (3n+5)(n+3).

The solutions, or zeroes, of any equation are where y=0. Therefore, we set the expression 3n^2+14n+15=0, or (3n+5)(n+3)=0. To obtain zero from two products, either of the products must equal zero. Therefore, we can state 3n+5=0 and n+3=0. Solving these equations, we get:

3n+5=0
3n=-5
n=-5/3

and

n+3=0
n=-3.

Finally, the solutions are n=-5/3 and n=-3