y^4-18y^2+72=0

Solution for y^4-18y^2+72=0 equation:

Simplifying
y4 + -18y2 + 72 = 0

Reorder the terms:
72 + -18y2 + y4 = 0

Solving
72 + -18y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + -1y2)(12 + -1y2) = 0

Subproblem 1
Set the factor '(6 + -1y2)' equal to zero and attempt to solve:

Simplifying
6 + -1y2 = 0

Solving
6 + -1y2 = 0

Move all terms containing y to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y2 = 0 + -6
-1y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1y2 = -6

Divide each side by '-1'.
y2 = 6

Simplifying
y2 = 6

Take the square root of each side:
y = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(12 + -1y2)' equal to zero and attempt to solve:

Simplifying
12 + -1y2 = 0

Solving
12 + -1y2 = 0

Move all terms containing y to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1y2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y2 = 0 + -12
-1y2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1y2 = -12

Divide each side by '-1'.
y2 = 12

Simplifying
y2 = 12

Take the square root of each side:
y = {-3.464101615, 3.464101615}
Solution
y = {-2.449489743, 2.449489743, -3.464101615, 3.464101615}