Question 325076
Factor out the largest common factor.
t^5 - 8t^4
-8t^4+t^5  Usually the order is descending exponents.  It's not wrong, but there's no reason to change the order.
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t^4(-8+t)=0 t4 is the gcf  *** you wrote an equation???  why?
You factored correctly.  Neither of the 2 factors is consistently the greatest.  The problem should have said, "factor", without reference to the gcf.
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The rest is NA.  No equation was given, no solutions asked for.
t4=0
(-8+t)
-8+t=0
add 8 to each side 
-8+8+t=0+8
-8+8=0+8
t=0+8
0+8=8
T=8