I am trying to solve following polynomial equations using solve
However it returns an empty set.

```
    `3*d*x**2 + 2*w*x = 0,` 
    `3*d*y**2 + 2*w*y = 0,`
    `-d + 2*w*z + 1 =0,`
    `x**3 + y**3 - z = 0,`
    `x**2 + y**2 + z**2 - 1 = 0`

```

wolfram-alpha returns following real solutions.

```
    `d≈0.417238, w≈-0.516977, x = 0, y≈0.826031, z≈0.563624`
    `d≈0.417238, w≈-0.516977, x≈0.826031, y = 0, z≈0.563624`
    `d≈0.417238, w≈0.516977, x = 0, y≈-0.826031, z≈-0.563624`
    `d≈0.417238, w≈0.516977, x≈-0.826031, y = 0, z≈-0.563624`
    `d≈0.528689, w≈-0.492358, x≈0.620853, y≈0.620853, z≈0.478626`

```

How do I ensure that I get the solutions if they exist ?
Is there any other method with more robust handling of 0 and other conditions?