25x^3-5x^2+10x=0

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Solution for 25x^3-5x^2+10x=0 equation: 


Simplifying
25x3 + -5x2 + 10x = 0

Reorder the terms:
10x + -5x2 + 25x3 = 0

Solving
10x + -5x2 + 25x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(2 + -1x + 5x2) = 0

Ignore the factor 5.

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 '(2 + -1x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + 5x2 = 0

Solving
2 + -1x + 5x2 = 0

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

Divide each side by '5'.
0.4 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -0.2x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -0.2x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -0.2x + x2 = 0 + -0.4
-0.2x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-0.2x + x2 = -0.4

The x term is -0.2x.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2x + 0.01 + x2 = -0.4 + 0.01

Reorder the terms:
0.01 + -0.2x + x2 = -0.4 + 0.01

Combine like terms: -0.4 + 0.01 = -0.39
0.01 + -0.2x + x2 = -0.39

Factor a perfect square on the left side:
(x + -0.1)(x + -0.1) = -0.39

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}

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