6x(4x^2-3x+1)=0

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Solution for 6x(4x^2-3x+1)=0 equation: 


Simplifying
6x(4x2 + -3x + 1) = 0

Reorder the terms:
6x(1 + -3x + 4x2) = 0
(1 * 6x + -3x * 6x + 4x2 * 6x) = 0
(6x + -18x2 + 24x3) = 0

Solving
6x + -18x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(1 + -3x + 4x2) = 0

Ignore the factor 6.

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 '(1 + -3x + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + -3x + 4x2 = 0

Solving
1 + -3x + 4x2 = 0

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

Divide each side by '4'.
0.25 + -0.75x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -0.75x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -0.75x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -0.75x + x2 = 0 + -0.25
-0.75x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-0.75x + x2 = -0.25

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = -0.25 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = -0.25 + 0.140625

Combine like terms: -0.25 + 0.140625 = -0.109375
0.140625 + -0.75x + x2 = -0.109375

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = -0.109375

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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