Answer:
x = -3, -2, 0
Explanation:
To solve for x, you need to factorise.
When factorising, the first thing you need to do is check for anything all terms have in common. Here the terms have 'x' in common, so we can do this:
x³+5x²+6x=0
x(x²+5x+6)=0
Now let's factorise what's in the brackets, x²+5x+6. Factorising an expression in the form x²+bx+c, leaves us a pair of brackets of the form (x+d)(x+e) where d+e=b and (d)(e)=c. So we get:
x²+5x+6=(x+2)(x+3)
So now we know x³+5x²+6x= x((x+2)(x+3) = 0. Since the expression is equal to zero, and the only way for the product of multiplication to be zero is if one of the terms being multiplied is zero, we know either x, x+2, and x+3 is equal to zero.
So our solutions for x are:
x=0
x+2=0, x=-2
x+3=0, x=-3