y^4+24y^2-1225=0

Solution for y^4+24y^2-1225=0 equation:

Simplifying
y4 + 24y2 + -1225 = 0

Reorder the terms:
-1225 + 24y2 + y4 = 0

Solving
-1225 + 24y2 + y4 = 0

Solving for variable 'y'.

Factor a trinomial.
(-49 + -1y2)(25 + -1y2) = 0

Factor a difference between two squares.
(-49 + -1y2)((5 + y)(5 + -1y)) = 0

Subproblem 1
Set the factor '(-49 + -1y2)' equal to zero and attempt to solve:

Simplifying
-49 + -1y2 = 0

Solving
-49 + -1y2 = 0

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

Add '49' to each side of the equation.
-49 + 49 + -1y2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -1y2 = 0 + 49
-1y2 = 0 + 49

Combine like terms: 0 + 49 = 49
-1y2 = 49

Divide each side by '-1'.
y2 = -49

Simplifying
y2 = -49

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Subproblem 3
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-5, 5}