Question

How do you solve `x^4+3x^3-4x^2+12=0`?

Answer 1

Since this polynomial has no easily determined solutions and no further clarification was provided, I've employed an "engineer"-type solution to clear out this question.

Explanation:

Note that I dropped the `=0` portion of the given equality to make it a polynomial function.

Using a graphing package I can establish the x-intercepts at approximately `x=-1.38` and `x=-3.831` (there are only 2 intercepts)
Based on these values `{(f(x) > 0,"if " x < -3.831),(f(x) < 0,"if "x in (-3.831,-1.38)),(f(x) > 0,"if "x > -1.38):}`

We could now test using values `x in{-5,-2,0}`
but using the graph, this is not really necessary.

Here is the graph at a moderate scale (I had to blow it up significantly to get approximations for the x-intercept values):