Question 164069
<pre><font size = 4 color = "indigo"><b>{{{x^3 + 2x^2 - 9x = 18}}}

{{{x^3 + 2x^2 - 9x - 18=0}}}

Factor {{{x^2}}} out of the first two terms:

{{{x^2(x + 2) - 9x - 18=0}}}

Factor {{{-9}}} out of the last two terms:

{{{x^2(x + 2) - 9(x +2)=0}}}

Factor {{{(x+2)}}} out of each term:

{{{(x + 2)(x^2 - 9)=0}}}

Factor the second parentheses as the difference of two squares:

{{{(x + 2)(x-3)(x+3)=0}}}

Use the zero-factor principle:

{{{matrix(2,5,    x+2=0 ,  "," ,  x-3=0 ,  "," ,  x+3=0 ,
               x=-2 ,  "," ,    x=3 ,  "," ,   x=-3  )}}}
   
Edwin</pre>