I can't find anything to help solve this in my notes.

The deflection y of a beam at a horizontal distance x from one end is given by the equation below, where L is the length of the beam and k is a constant. For what values of x is the deflection zero?
y = k(x^4 – 8Lx^3 + 7L^3x)
For what values of x is the deflection zero?

Question

I can't find anything to help solve this in my notes.

The deflection y of a beam at a horizontal distance x from one end is given by the equation below, where L is the length of the beam and k is a constant.  For what values of x is the deflection zero?
y = k(x^4 – 8Lx^3 + 7L^3x)
For what values of x is the deflection zero?

paxpolaris · Answer

$$\Large 0 = \cancel k\left( x^4 – 8Lx^3 + 7L^3x \right) $$
$$\Large \implies x\left( x^3 – 8Lx^2 + 7L^3 \right)=0$$

keep factoring for answer