Question 72957
{{{m*(m^2+2m-3=0}}}
.
So far you are correct.
.
The next thing you can do is notice that the term {{{m^2 + 2m -3}}} can be factored. It
factors into {{{(m + 3)*(m - 1)}}}.
.
Now you can return to your equation and substitute these factors for {{{m^2 + 2m -3}}} and 
you will then have:
.
{{{m*(m+3)*(m-1) = 0}}}
.
Notice that this equation will be true if any of the factors on the left side equals zero.
This is because a zero factor on the left side is a multiplier and it will make the whole
left side equal to zero which is also the right side.  Therefore, with a zero factor the
equation is balanced because 0 equals 0 is the result.
.
So all you have to do is set each of the three factors equal to zero and solve for m.
.
The first factor is m and setting it equal to zero says: {{{m = 0}}}. This becomes one
of the answers.
.
The second factor is {{{m + 3}}} and setting it equal to zero results in: {{{m + 3 = 0}}}. You
can solve for m by subtracting +3 from both sides to get rid of the +3 on the left side.
When you subtract +3 from both sides you get {{{m = -3}}} and that is the second answer.
.
Finally, the third factor is {{{m - 1}}} and setting it equal to zero gives you the equation
{{{m - 1 = 0}}}.  You can solve this equation for m by adding 1 to both sides to eliminate the
-1 on the left side.  Adding +1 to both sides of this equation results in {{{m = +1}}}.
.
So the three possible answers for m are 0, -3, and +1.  Each of these three can be substituted
back into the original equation given in the problem, and that equation will become
equal on both sides.
.
I hope this helps you understand the problem a little more.  The hardest part of this problem
was to recognize that you could factor the quadratic terms and then to find the factors. It
takes a lot of practice to do this and you are well on your way to getting it.  Keep up the
good work!