Nonlinear Equation solved w/ grouping: y^3-16y=5y^2-80

[flappergirl68]

I started w/ the problem

y^3-16y=5y^2-80

which I've moved to one side to make

y^3-5y^2-16y+80=0

and I'm stuck and cannot figure out the proper way to group this and go on!
Any ideas?
-thanks

 

[arthur ohlsten]

I suggest in all such problems you group the odd exponents and the even exponents.

y^3-5y^2-16y+80=0 regroup
[y^3-16y] + [-5y^2+80]=0
factor out a y from first bracket and -5 from second bracket
y[y^2-16] -5[y^2-16]=0
factor out [y^2-16]
[y^2-16][y-5]=0
factor y^2-16
[y-4][y+4][y-5]=0
y=4,-4,5 answer

Arthur

group odd and even exponents! ok?

 

[Mrspi]

I started w/ the problem

y^3-16y=5y^2-80

which I've moved to one side to make

y^3-5y^2-16y+80=0

and I'm stuck and cannot figure out the proper way to group this and go on!
Any ideas?
-thanks

I'd group the first two terms, and the last two terms:

y^3 - 5y^2 - 16y + 80 = 0

You can remove a common factor of y^2 out of the first two terms, and a common factor of -16 out of the last two terms:

y^2 (y - 5) -16(y - 5) = 0

Can you take it from here?