x^3-7x=0

Solution for x^3-7x=0 equation:

Simplifying
x3 + -7x = 0

Reorder the terms:
-7x + x3 = 0

Solving
-7x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + x2) = 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 '(-7 + x2)' equal to zero and attempt to solve:

Simplifying
-7 + x2 = 0

Solving
-7 + x2 = 0

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

Add '7' to each side of the equation.
-7 + 7 + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x2 = 0 + 7
x2 = 0 + 7

Combine like terms: 0 + 7 = 7
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {0, -2.645751311, 2.645751311}