z^4-12z^2+72=0

Solution for z^4-12z^2+72=0 equation:

Simplifying
z4 + -12z2 + 72 = 0

Reorder the terms:
72 + -12z2 + z4 = 0

Solving
72 + -12z2 + z4 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -12z2 + -72 + z4 = 0 + -72

Reorder the terms:
72 + -72 + -12z2 + z4 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -12z2 + z4 = 0 + -72
-12z2 + z4 = 0 + -72

Combine like terms: 0 + -72 = -72
-12z2 + z4 = -72

The z term is -12z2.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12z2 + 36 + z4 = -72 + 36

Reorder the terms:
36 + -12z2 + z4 = -72 + 36

Combine like terms: -72 + 36 = -36
36 + -12z2 + z4 = -36

Factor a perfect square on the left side:
(z2 + -6)(z2 + -6) = -36

Can't calculate square root of the right side.

The solution to this equation could not be determined.