50x-x^3=0

Solution for 50x-x^3=0 equation:

Simplifying
50x + -1x3 = 0

Solving
50x + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(50 + -1x2) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(50 + -1x2)' equal to zero and attempt to solve:

Simplifying
50 + -1x2 = 0

Solving
50 + -1x2 = 0

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

Add '-50' to each side of the equation.
50 + -50 + -1x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -1x2 = 0 + -50
-1x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-1x2 = -50

Divide each side by '-1'.
x2 = 50

Simplifying
x2 = 50

Take the square root of each side:
x = {-7.071067812, 7.071067812}
Solution
x = {0, -7.071067812, 7.071067812}