Algebra 2 honors help please help!!!!!:)

Can someone explain to me step by step how to solve
1)125x to the power of 3-7=o
2)x to the power of 3 +2x squared+5x+10=0
Thanks for the help!!!

125 x^3 -7 = 0
125 x^3 -7 +7 = 0 +7
125 x^3 = 7
x^3 = 7/125
now to solve for x we need to take the cubed root. We know that the cubed root of 125 is 5 because 5^3 = (5) (5) (5) = 125 but there is no cubed root of 7 so we can rewrite the equation as follows.

x =(1/5)(cubed root of 7)
or
x = (1/5) {7^(1/3)}


NEXT PROBLEM
x^3 + 2x^2 +5x +10 = 0
x^2(x +2) + 5(x+2) = 0
(x^2 +5) (x+2) = 0
x^2 +5 = 0 and (x+2) = 0

Solving for x^2 +5 = 0
x^2 +5 -5 = 0 -5
x^2 = -5
x = sqrt (-5)
x = i (sqrt (5)) {Remember that sqrt(-1) = i}

Solving for x+2 = 0
x = -2

So you have two answers for x.
x = i(sqrt(5)) and x= -2