Question 107254
First example. 
A quick graph of the function shows that x=-4 looks like a root of the equation.
{{{ graph( 300, 300, -5, 5, -10, 10, x^3+3x^2-5x-4) }}}
{{{f(x)=x^3+3x^2-5x-4}}}
{{{f(4)=(-4)^3+3*(-4)^2-5*(-4)-4}}}
{{{f(4)=-64+48+20-4}}}
{{{f(4)=0}}}
You can then find the polynomial g(x) such that
{{{f(x)=g(x)*(x+4)}}}
where {{{g(x)=ax^2+bx+c}}} and
{{{f(x)=(ax^2+bx+c)*(x+4)}}}
{{{f(x)=ax^3+(b+4a)x^2+(c+4b)*x+4c}}}
Compare that to your original equation.
{{{f(x)=x^3+3x^2-5x-4}}} and you see that
1.{{{a=1}}}
2.{{{b+4a=3}}}
3.{{{c+4b=-5}}}
4.{{{4c=-4}}}
From 1 and 2,
{{{b+4=3}}}
{{{b=-1}}}
From 4,
{{{4c=-4}}}
{{{c=-1}}}
{{{g(x)=x^2-x-1}}}
You can then find the roots of g(x) using the quadratic equation.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-(-1) +- sqrt( (-1)^2-4*1*(-1) ))/(2*1) }}} 
The roots of g(x) are then
{{{x = (1 +- sqrt(5))/(2) }}}
or approximately, x=-0.62 and x=1.62 

Second example.
A quick graph of the function shows that x=-3 and x=3 look like roots of the equation.
{{{ graph( 300, 300, -5, 5, -10, 10, x^4-2x^3-7x^2+18x-18) }}}
{{{h(x)=x^4-2x^3-7x^2+18x-18}}}
{{{h(-3)=81+54-63-54-18}}}
{{{h(-3)=0}}}
{{{h(x)=x^4-2x^3-7x^2+18x-18}}}
{{{h(3)=81-54-63+54-18}}}
{{{h(3)=0}}}
So then you can rewrite your equation to look like. 
{{{h(x)=g(x)*(x+3)*(x-3)}}}
where 
{{{g(x)=ax^2+bx+c}}}
Follow the first example above to find a,b,and c. 
Post another question if you get stuck. 
Good luck.