Question 153127

I'm assuming that the equation should look like this: {{{x^3+2x^2-36x-72=0}}}
 


{{{x^3+2x^2-36x-72=0}}} Start with the given expression



{{{(x^3+2x^2)+(-36x-72)=0}}} Group like terms



{{{x^2(x+2)-36(x+2)=0}}} Factor out the GCF {{{x^2}}} out of the first group. Factor out the GCF {{{-36}}} out of the second group



{{{(x^2-36)(x+2)=0}}} Since we have the common term {{{x+2}}}, we can combine like terms



{{{(x+6)(x-6)(x+2)=0}}} Factor {{{x^2-36}}} to get {{{(x+6)(x-6)}}}



Now set each factor equal to zero:


{{{x+6=0}}}, {{{x-6=0}}} or {{{x+2=0}}}



Now solve for x for each factor:



{{{x=-6}}}, {{{x=6}}} or {{{x=-2}}}



So the solutions are {{{x=-6}}}, {{{x=6}}} or {{{x=-2}}}