y^4-14y^2+40=0

Solution for y^4-14y^2+40=0 equation:

Simplifying
y4 + -14y2 + 40 = 0

Reorder the terms:
40 + -14y2 + y4 = 0

Solving
40 + -14y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y2)(10 + -1y2) = 0

Factor a difference between two squares.
((2 + y)(2 + -1y))(10 + -1y2) = 0

Subproblem 1
Set the factor '(10 + -1y2)' equal to zero and attempt to solve:

Simplifying
10 + -1y2 = 0

Solving
10 + -1y2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y2 = 0 + -10
-1y2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1y2 = -10

Divide each side by '-1'.
y2 = 10

Simplifying
y2 = 10

Take the square root of each side:
y = {-3.16227766, 3.16227766}
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Subproblem 3
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-3.16227766, 3.16227766, -2, 2}