2x^3-50x+1=1

Solution for 2x^3-50x+1=1 equation:

Simplifying
2x3 + -50x + 1 = 1

Reorder the terms:
1 + -50x + 2x3 = 1

Add '-1' to each side of the equation.
1 + -50x + -1 + 2x3 = 1 + -1

Reorder the terms:
1 + -1 + -50x + 2x3 = 1 + -1

Combine like terms: 1 + -1 = 0
0 + -50x + 2x3 = 1 + -1
-50x + 2x3 = 1 + -1

Combine like terms: 1 + -1 = 0
-50x + 2x3 = 0

Solving
-50x + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-25 + x2) = 0

Factor a difference between two squares.
2x((5 + x)(-5 + x)) = 0

Ignore the factor 2.
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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

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

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Solution
x = {0, -5, 5}