63x^5-70x^3+15x=0

Solution for 63x^5-70x^3+15x=0 equation:

Simplifying
63x5 + -70x3 + 15x = 0

Reorder the terms:
15x + -70x3 + 63x5 = 0

Solving
15x + -70x3 + 63x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(15 + -70x2 + 63x4) = 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 '(15 + -70x2 + 63x4)' equal to zero and attempt to solve:

Simplifying
15 + -70x2 + 63x4 = 0

Solving
15 + -70x2 + 63x4 = 0

Begin completing the square.  Divide all terms by
63 the coefficient of the squared term: 

Divide each side by '63'.
0.2380952381 + -1.111111111x2 + x4 = 0

Move the constant term to the right:

Add '-0.2380952381' to each side of the equation.
0.2380952381 + -1.111111111x2 + -0.2380952381 + x4 = 0 + -0.2380952381

Reorder the terms:
0.2380952381 + -0.2380952381 + -1.111111111x2 + x4 = 0 + -0.2380952381

Combine like terms: 0.2380952381 + -0.2380952381 = 0.0000000000
0.0000000000 + -1.111111111x2 + x4 = 0 + -0.2380952381
-1.111111111x2 + x4 = 0 + -0.2380952381

Combine like terms: 0 + -0.2380952381 = -0.2380952381
-1.111111111x2 + x4 = -0.2380952381

The x term is -1.111111111x2.  Take half its coefficient (-0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
-1.111111111x2 + 0.3086419752 + x4 = -0.2380952381 + 0.3086419752

Reorder the terms:
0.3086419752 + -1.111111111x2 + x4 = -0.2380952381 + 0.3086419752

Combine like terms: -0.2380952381 + 0.3086419752 = 0.0705467371
0.3086419752 + -1.111111111x2 + x4 = 0.0705467371

Factor a perfect square on the left side:
(x2 + -0.5555555555)(x2 + -0.5555555555) = 0.0705467371

Calculate the square root of the right side: 0.265606357

Break this problem into two subproblems by setting 
(x2 + -0.5555555555) equal to 0.265606357 and -0.265606357.

Subproblem 1
x2 + -0.5555555555 = 0.265606357

Simplifying
x2 + -0.5555555555 = 0.265606357

Reorder the terms:
-0.5555555555 + x2 = 0.265606357

Solving
-0.5555555555 + x2 = 0.265606357

Solving for variable 'x'.

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

Add '0.5555555555' to each side of the equation.
-0.5555555555 + 0.5555555555 + x2 = 0.265606357 + 0.5555555555

Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000
0.0000000000 + x2 = 0.265606357 + 0.5555555555
x2 = 0.265606357 + 0.5555555555

Combine like terms: 0.265606357 + 0.5555555555 = 0.8211619125
x2 = 0.8211619125

Simplifying
x2 = 0.8211619125

Take the square root of each side:
x = {-0.906179846, 0.906179846}

Subproblem 2
x2 + -0.5555555555 = -0.265606357

Simplifying
x2 + -0.5555555555 = -0.265606357

Reorder the terms:
-0.5555555555 + x2 = -0.265606357

Solving
-0.5555555555 + x2 = -0.265606357

Solving for variable 'x'.

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

Add '0.5555555555' to each side of the equation.
-0.5555555555 + 0.5555555555 + x2 = -0.265606357 + 0.5555555555

Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000
0.0000000000 + x2 = -0.265606357 + 0.5555555555
x2 = -0.265606357 + 0.5555555555

Combine like terms: -0.265606357 + 0.5555555555 = 0.2899491985
x2 = 0.2899491985

Simplifying
x2 = 0.2899491985

Take the square root of each side:
x = {-0.538469311, 0.538469311}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.906179846, 0.906179846, -0.538469311, 0.538469311}
Solution
x = {0, -0.906179846, 0.906179846, -0.538469311, 0.538469311}