125x^3+13x=10x^2

Solution for 125x^3+13x=10x^2 equation:

Simplifying
125x3 + 13x = 10x2

Reorder the terms:
13x + 125x3 = 10x2

Solving
13x + 125x3 = 10x2

Solving for variable 'x'.

Reorder the terms:
13x + -10x2 + 125x3 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
13x + -10x2 + 125x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + -10x + 125x2) = 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 '(13 + -10x + 125x2)' equal to zero and attempt to solve:

Simplifying
13 + -10x + 125x2 = 0

Solving
13 + -10x + 125x2 = 0

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

Divide each side by '125'.
0.104 + -0.08x + x2 = 0

Move the constant term to the right:

Add '-0.104' to each side of the equation.
0.104 + -0.08x + -0.104 + x2 = 0 + -0.104

Reorder the terms:
0.104 + -0.104 + -0.08x + x2 = 0 + -0.104

Combine like terms: 0.104 + -0.104 = 0.000
0.000 + -0.08x + x2 = 0 + -0.104
-0.08x + x2 = 0 + -0.104

Combine like terms: 0 + -0.104 = -0.104
-0.08x + x2 = -0.104

The x term is -0.08x.  Take half its coefficient (-0.04).
Square it (0.0016) and add it to both sides.

Add '0.0016' to each side of the equation.
-0.08x + 0.0016 + x2 = -0.104 + 0.0016

Reorder the terms:
0.0016 + -0.08x + x2 = -0.104 + 0.0016

Combine like terms: -0.104 + 0.0016 = -0.1024
0.0016 + -0.08x + x2 = -0.1024

Factor a perfect square on the left side:
(x + -0.04)(x + -0.04) = -0.1024

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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