y^3+10y+24y=0

Solution for y^3+10y+24y=0 equation:

Simplifying
y3 + 10y + 24y = 0

Reorder the terms:
10y + 24y + y3 = 0

Combine like terms: 10y + 24y = 34y
34y + y3 = 0

Solving
34y + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(34 + 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 '(34 + y2)' equal to zero and attempt to solve:

Simplifying
34 + y2 = 0

Solving
34 + y2 = 0

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

Add '-34' to each side of the equation.
34 + -34 + y2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + y2 = 0 + -34
y2 = 0 + -34

Combine like terms: 0 + -34 = -34
y2 = -34

Simplifying
y2 = -34

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}