Solve for all values of x by factoring.
x^2-x-8=-3x

The roots are {-4, 2}.

Step-by-step explanation:

It seems strange to have x terms on both sides of your equation.  If this is indeed the correct equation, then

x^2-x-8=-3x becomes x^2 +3x - x - 8= 0, and this latter result simplifies to

x^2 + 2x - 8 = 0.  

One set of factors of -8 is {-2, 4} and another is {1, -8).  Hence we could try evaluating this quadratic at x = 4:

4^2 + 2(4) - 8 = 16 (since this is not zero, 4 is not a root and (x - 4) is not a factor.  

Try x = -4 instead:

(-4)^2 + 2(-4) - 8 = 0 simplifies to 16 - 8 - 8 = 0, which is true.

Then x + 4 is a factor and x - 2 is another.  Multiplying these two together as a check results in the given x^2- x - 8 = -3x.

The roots are {-4, 2}.

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