Solve the following equation in the complex number system. Please show all of your work.
2x^5-3x^4-32x+48=0
solving quintics is hard, so look for easy roots with synthetic division
2x^5-3x^4-32x+48
(x+2)(x-2)(2x-3)(x^2+4)
= (x+2)(x-2)(2x-3)(x-2i)(x+2i)
The manager of a coffee shop has one type of coffee that sells for $5 per pound and another type that sells for
$11 per pound. The manager wishes to mix 60 pounds of the $11 coffee to get a mixture that will sell for $9 per
pound. How many pounds of the $5 coffee should be used?