How do i find the roots of this polynomial equation? The polynomial equation is: $x^4-5x^3+5x^2+5x-6=0$. 
How do i simplify this equation so that i can find its roots.
Please, can anyone teach me how to find roots of equations of degree 4 and degree 3.

A quartic polynomial is always of form $$ax^4+bx^3+cx^2+de+e$$.
Now we know that in a quartic equation the product of the roots is equal to $e/a$. Here $e$ is equal to $-6$ and the coefficient of $x^4$ is also 1 so the product of the zeroes is equal to $-6$. We also know that the sum of the zeroes of a quartic polynomial is equal to $-b/a$ and since here also $a$ is $1$ the sum of the zeroes is equal to $-b$ I.e $5$. Thus we conclude that we have to find a set of integers whose sum is $5$ and product is $-6$. Now you just need to factorise $-6$ which will be $2×3×1×-1$ .Now you are very lucky that you got exactly 4 factors which will stand for the $4$ zeroes of the polynomial. Now you need to arrange these numbers in a way that you get $5$ which we get through $2+3+1-1$ thus we get the zeroes of the polynomial as $2,3,1,-1$. 
If the coefficient of $x^4$ is not 1 then this method won't be good as you might get your zeroes in fractions which will be very difficult to operate upon. But this is the fastest method where $a=1$ . You can carry out this method for all polynomials where $a=1$ and easily get the roots.
