Help with 1 algebra problem ?

Question

solve the inequality and write the solution set in interval notation

(x-1)^2 * (x+2)^3 >= 0 (greater than or equal to)

please go step by step...the answer is [-2, {infinity} ) if that helps...but i need to show work

Answer 1

Clearly x=1 satisfies the inequality. ...(1)

Suppose x not = 1, then since (x-1)^2 is always positive, we have

(x+2)^3 >= 0

=> (x+2) >= 0

=> x > -2 ...(2)

Combining (1) and (2), we have [-2, inf)