tan^2(x)+tan(x) intersection points with axis x and y?

Thanks CPhill,

CPhill and I   have both interpreted your question to mean

$$y=tan^2x+tanx$$

If x=0 then y=0 because   tan0=0

If y=0 then

$$\\tanx(tanx+1)=0\\\\ tanx=0\;\;or\;\;tanx+1=0\\\\ sinx=0\;\;or\;\;tanx=-1\\\\ x=n\pi\pm \frac{\pi}{2}\;\;\;or\;\;\;x=n\pi\pm \frac{3\pi}{4}\qquad n\in Z$$

My answer is the same as CPhill"s

Here's a graph.........https://www.desmos.com/calculator/wpfchryj3k

This function  intersects the x axis   at    -45° + k*180°  and at   0° + k*180°  {where k is an integer}

It only intersects the y axis at the origin....!!!!