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.

.The key is  first substituting integral small values of $x$, which are factors of the constant term,  which is $6$. In this case, we try to substitute $1$. We see that if $f(x) = x^4-5x^3+5x^2+5x-6$, then: $f(1)=0$ and $f(-1)=0$. Hence, $x-1$ and $x+1$ are factors of $x^4-5x^3+5x^2+5x-6$.
Now perform polynomial division: divide $ x^4-5x^3+5x^2+5x-6$ by the product $(x-1)(x+1) = x^2-1$, and you should get $(x^2-5x+6)$. Once this is done, you can either use the quadratic formula, or the same technique as above to see that $2$ and $3$ are roots of $x^2-5x+6$, which means that $x^2-5x+6 = (x-2)(x-3)$.
Hence, $f(x) = (x+1)(x-1)(x-2)(x-3)$.
If it were a general cubic or quartic equation, then although formulas (like Cardano) are known, they are cumbersome to say the least, and very hard to work out on hand. So if you get a problem like this to solve by hand, it is most likely either an observation or hit-and-trial with the factors of the constant term (if there is no constant term, then $x$ is a factor, so divide by $x$ until you get a constant term) that is likely to give a breakthrough.
