$f(x)=x^6 +4x^5 -6x^4-32x^3+ax^2$

$y=m\cdot x+c$ 

where $m$ is the gradient and $c$ is the $y$-intercept

The question is that the function $f(x)$ has three $x$ values where it touches the tangent line given by $y=m\cdot x +c$

What would be a in order for this to happen?

And what is the tangent line's equation?