Hi,
1) z^4 + 8z^3 - 9z^2 = 0
always begin by looking for a common factor in the terms
z^2(z^2 + 8 - 9) = 0
factor trinomial as two products if possible
z^2(z+9)(z-1)
roots are x= 0, x= -9 x = 1
2)(y - 7)(2y^ + 7 - 15) = 0
factor trinomial as two products if possible
(y - 7)(2y^ + 7 - 15) = 0
(y - 7)(2y^ -3)(y + 5) = 0
roots are y = 7, y = 3/2 and y = -5