y^6+13y^5-48y^4=0

Solution for y^6+13y^5-48y^4=0 equation:

Simplifying
y6 + 13y5 + -48y4 = 0

Reorder the terms:
-48y4 + 13y5 + y6 = 0

Solving
-48y4 + 13y5 + y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y4'.
y4(-48 + 13y + y2) = 0

Factor a trinomial.
y4((-16 + -1y)(3 + -1y)) = 0

Subproblem 1
Set the factor 'y4' equal to zero and attempt to solve:

Simplifying
y4 = 0

Solving
y4 = 0

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

Simplifying
y4 = 0

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 '(-16 + -1y)' equal to zero and attempt to solve:

Simplifying
-16 + -1y = 0

Solving
-16 + -1y = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1y = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1y = 0 + 16
-1y = 0 + 16

Combine like terms: 0 + 16 = 16
-1y = 16

Divide each side by '-1'.
y = -16

Simplifying
y = -16
Subproblem 3
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-16, 3}