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Equations of the form z^4+az^2+a_0 are known as biquadratic equations. They are quartic equations. In general they can be solved by reducing them to a quadratic equation where x=z^2 is the variable. Then you can use the quadratic formula or factor. So plugging in x to the biquadratic giives us x^2+ax+a_0.
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What is quartic and biquadratic?
A quartic is a polynomial of degree 4, meaning the highest exponent is 4. Biquadratic can mean the same thing, but most mathematicians use the term biquadratic to refer to an equation of degree 4 with no odd powers. So for example we cannot have an x3 term. An example of a biquadratic is: x4 +x2 + 22=0
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