y^3-66y+13y=0

Solution for y^3-66y+13y=0 equation:

Simplifying
y3 + -66y + 13y = 0

Reorder the terms:
-66y + 13y + y3 = 0

Combine like terms: -66y + 13y = -53y
-53y + y3 = 0

Solving
-53y + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-53 + y2) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-53 + y2)' equal to zero and attempt to solve:

Simplifying
-53 + y2 = 0

Solving
-53 + y2 = 0

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

Add '53' to each side of the equation.
-53 + 53 + y2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + y2 = 0 + 53
y2 = 0 + 53

Combine like terms: 0 + 53 = 53
y2 = 53

Simplifying
y2 = 53

Take the square root of each side:
y = {-7.280109889, 7.280109889}
Solution
y = {0, -7.280109889, 7.280109889}