Question 170149

{{{5t^2+30t-5t^3=0}}} Start with the given equation



{{{-5t^3+5t^2+30t=0}}} Rearrange the terms.



{{{-5t(t^2-t-6)=0}}} Factor out the GCF -5t



{{{-5t=0}}} or {{{t^2-t-6=0}}} Set each factor equal to zero
 


{{{t=0}}} Solve the first equation for "t" by dividing both sides by -5



So the first solution is {{{t=0}}}



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Now let's solve the second equation {{{t^2-t-6=0}}} 



{{{t^2-t-6=0}}} Start with the given equation


{{{(t-3)(t+2)=0}}} Factor the left side (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{t-3=0}}} or  {{{t+2=0}}} 


{{{t=3}}} or  {{{t=-2}}}    Now solve for t in each case



So next two solutions are 


 {{{t=3}}} or  {{{t=-2}}} 




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Answer:


So the solutions are {{{t=0}}}, {{{t=3}}} or  {{{t=-2}}}