Is there a typo here? Maybe it should be 0 = x^3 + 6x^2 -3x - 18 . This can be solved by grouping like so:
0 = (x^3 + 6x^2) + (-3x - 18 ) This is the grouping step. I groupred the first two terms, and the last two terms.
0 = x^2(x+6) - 3(x+6) In this step, I factored out the greatest common factor from each set of parenthesis.
0 = ( x+6 )(x^2 - 3) In this step, I factored out the common (x+6) binomial factor from the right side of the equation.
(a challenging notion to follow, but it goes something like this: In x^2(x+6) - 3(x+6) , think of x^2 as "a", 3 as "b", and (x+6) as "c", Then x^2(x+6) - 3(x+6) is of the form ac - bc. I factored out the "c" to get c(a-b). Substituting back, using x^2 as "a", 3 as "b", and (x+6) as "c", get c(a-b) = (x+6)(x^2-3)
Continuing on to solve the equation, if 0 = ( x+6 )(x^2 - 3) , then
0 = x+6 or 0 = x^2 -3
Solving these equations, get x = -6, x =sqrt(3), x = - sqrt(3) (remember when taking the square root of each side you must include both the positive and negative results)