how do you solve: x^3-18x^2<0?

x^3 - 18x^2 < 0

solve
x^3 - 18x^2 = 0
x^2(x - 18) = 0

x^2 =0 OR x - 18 = 0
x = 0 OR x = 18

touches X axis at x = 0
&
crosses X axis at x = 18
=> x^3-18x^2<0

x<0 & 0 < x < 18


P.S.
above answers incorrect as x=/= 0

QED

x^3 - 18x^2 < 0

First you factor out an x:

x(x^2-18x) < 0

x^2-18x can once again factor out another x:

x(x-18)

Therefore:

x^3 - 18x^2 < 0 is equal to

(x)(x)(x-18) < 0

As you can see there are 3 sections
Let each section be its own equation:
x < 0
x < 0
x-18 < 0

Then solve each equation which would give you multiple answers.
In this case there are two:
x < 0
x < 18

Hope my answer helped

x^3 - 18x^2 < 0
x^2(x - 18) < 0

x^2 < 0
x < 0

x - 18 < 0
x < 18

∴ x < 0, x < 18

x^2(x-18) < 0

x < 18