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I have this code

Manipulate[ContourPlot[x^2 (z + 1) - (x + 1)^2 (z - 3 x^3) == 0, 
{x, -v, v}, {z, -w, w}], {v, 1, 50}, {w, 1, 50}]

to interactively make zoom in any axis of the graph defined by the equation $x^2(z+1)-(x+1)^2(z-3x^3)=0$. However when I move the slide of $v$ to the right the graph becomes ugly and full of spikes. I don't think this graph represent the equation above, so there is some weird evaluation somewhere.

There is a way to fix the behavior of Wolfram Mathematica for this kind of plots? In other way, there is a way to get a good graph of the above equation when the range of $x$ increases?

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Manipulate[ ContourPlot[x^2 (z + 1) - (x + 1)^2 (z - 3 x^3) == 0, {x, -v, v}, {z, -w, w}, 
  PlotPoints -> 100, PerformanceGoal -> "Quality"],
 {v, 1, 50}, {w, 1, 50}]

enter image description here

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You can use MaxRecursion. It will make the plots smother, but takes more time.

Manipulate[ContourPlot[x^2 (z + 1) - (x + 1)^2 (z - 3 x^3) == 0, {x, -v, v}, {z, -w, w}, 
MaxRecursion -> 5], {v, 1, 50}, {w, 1, 50}]
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