2x(6x^3-x^2+5x)=0

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Solution for 2x(6x^3-x^2+5x)=0 equation: 


Simplifying
2x(6x3 + -1x2 + 5x) = 0

Reorder the terms:
2x(5x + -1x2 + 6x3) = 0
(5x * 2x + -1x2 * 2x + 6x3 * 2x) = 0
(10x2 + -2x3 + 12x4) = 0

Solving
10x2 + -2x3 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(5 + -1x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(5 + -1x + 6x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x + 6x2 = 0

Solving
5 + -1x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + -0.1666666667x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + -0.1666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + -0.1666666667x + x2 = 0 + -0.8333333333
-0.1666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
-0.1666666667x + x2 = -0.8333333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = -0.8333333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = -0.8333333333 + 0.006944444447

Combine like terms: -0.8333333333 + 0.006944444447 = -0.826388888853
0.006944444447 + -0.1666666667x + x2 = -0.826388888853

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = -0.826388888853

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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