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

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


Simplifying
(2x + -4)(3x + -6) + 4 = 0

Reorder the terms:
(-4 + 2x)(3x + -6) + 4 = 0

Reorder the terms:
(-4 + 2x)(-6 + 3x) + 4 = 0

Multiply (-4 + 2x) * (-6 + 3x)
(-4(-6 + 3x) + 2x * (-6 + 3x)) + 4 = 0
((-6 * -4 + 3x * -4) + 2x * (-6 + 3x)) + 4 = 0
((24 + -12x) + 2x * (-6 + 3x)) + 4 = 0
(24 + -12x + (-6 * 2x + 3x * 2x)) + 4 = 0
(24 + -12x + (-12x + 6x2)) + 4 = 0

Combine like terms: -12x + -12x = -24x
(24 + -24x + 6x2) + 4 = 0

Reorder the terms:
24 + 4 + -24x + 6x2 = 0

Combine like terms: 24 + 4 = 28
28 + -24x + 6x2 = 0

Solving
28 + -24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -12x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + -12x + 3x2)' equal to zero and attempt to solve:

Simplifying
14 + -12x + 3x2 = 0

Solving
14 + -12x + 3x2 = 0

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

Divide each side by '3'.
4.666666667 + -4x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + -4x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + -4x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + -4x + x2 = 0 + -4.666666667
-4x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
-4x + x2 = -4.666666667

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -4.666666667 + 4

Reorder the terms:
4 + -4x + x2 = -4.666666667 + 4

Combine like terms: -4.666666667 + 4 = -0.666666667
4 + -4x + x2 = -0.666666667

Factor a perfect square on the left side:
(x + -2)(x + -2) = -0.666666667

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.

The solution to this equation could not be determined.

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