Can someone please explain to me how to do this problem. Thank You.
2x^2-3x-5=0
the numbers here are easy enough to do trial and error with. you should have (2x + a)(x + b) = 0
now, you want a and b such that a*b = -5 and a + 2b = -3
or if trial and error isn't your thing. try the ac method.
multiply the a and c terms, that is the $\displaystyle 2x^2$ and the $\displaystyle -5$, you get $\displaystyle -10x^2$
now you want two numbers that when you multiply them you get $\displaystyle -10x^2$ and when you add them you get the middle term ($\displaystyle -3x$). note that $\displaystyle -5x$ and $\displaystyle +2x$ works.
split the middle term into these two numbers, you get
$\displaystyle 2x^2 + 2x - 5x - 5 = 0$
factor the left side by grouping, you get
$\displaystyle 2x(x + 1) - 5(x + 1) = 0$
$\displaystyle \Rightarrow (x + 1)(2x - 5) = 0$
now continue using the zero-factor property