Question 124943

{{{a^2-3=2a}}} Start with the given equation



{{{a^2-3-2a=0}}}  Subtract 2a from both sides. 



{{{a^2-2a-3=0}}} Rearrange the terms


{{{(a-3)(a+1)=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:

{{{a-3=0}}} or  {{{a+1=0}}} 


{{{a=3}}} or  {{{a=-1}}}    Now solve for a in each case



So our answer is 

 {{{a=3}}} or  {{{a=-1}}} 



Notice if we graph {{{y=x^2-2x-3}}}  (just replace a with x)  we can see that the roots are {{{x=3}}} and  {{{x=-1}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^2-2x-3) }}}