Tangent line to a graph that is parallel to another line

Question

Consider the function h(x)= (1/4)x^4-(5/3)x^3+3x^2+4x. Find all values of x where the tangent line to the graph of y= h(x) is parallel to the line y= 4x+3

I found the derivative but now I don't know what to do from here h'(x)= x^3-5x^2+6x+4

Answer 1

Two lines are parallel if and only if they have the same slopes. That is,

$$x^3-5x^2+6x+4=4$$

In other words,

$$x(x^2-5x+6)=0,$$

or

$$x(x-3)(x-2)=0.$$

Now, I believe everything is clear.