4x(2x^2-6x+5)=0

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Solution for 4x(2x^2-6x+5)=0 equation: 


Simplifying
4x(2x2 + -6x + 5) = 0

Reorder the terms:
4x(5 + -6x + 2x2) = 0
(5 * 4x + -6x * 4x + 2x2 * 4x) = 0
(20x + -24x2 + 8x3) = 0

Solving
20x + -24x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + -6x + 2x2) = 0

Ignore the factor 4.

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 '(5 + -6x + 2x2)' equal to zero and attempt to solve:

Simplifying
5 + -6x + 2x2 = 0

Solving
5 + -6x + 2x2 = 0

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

Divide each side by '2'.
2.5 + -3x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + -3x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + -3x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + -3x + x2 = 0 + -2.5
-3x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
-3x + x2 = -2.5

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -2.5 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -2.5 + 2.25

Combine like terms: -2.5 + 2.25 = -0.25
2.25 + -3x + x2 = -0.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -0.25

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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