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

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


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

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

Multiply (-6 + 2x) * (4 + -2x)
(-6(4 + -2x) + 2x * (4 + -2x)) = (4x + -3)(x + 3)
((4 * -6 + -2x * -6) + 2x * (4 + -2x)) = (4x + -3)(x + 3)
((-24 + 12x) + 2x * (4 + -2x)) = (4x + -3)(x + 3)
(-24 + 12x + (4 * 2x + -2x * 2x)) = (4x + -3)(x + 3)
(-24 + 12x + (8x + -4x2)) = (4x + -3)(x + 3)

Combine like terms: 12x + 8x = 20x
(-24 + 20x + -4x2) = (4x + -3)(x + 3)

Reorder the terms:
-24 + 20x + -4x2 = (-3 + 4x)(x + 3)

Reorder the terms:
-24 + 20x + -4x2 = (-3 + 4x)(3 + x)

Multiply (-3 + 4x) * (3 + x)
-24 + 20x + -4x2 = (-3(3 + x) + 4x * (3 + x))
-24 + 20x + -4x2 = ((3 * -3 + x * -3) + 4x * (3 + x))
-24 + 20x + -4x2 = ((-9 + -3x) + 4x * (3 + x))
-24 + 20x + -4x2 = (-9 + -3x + (3 * 4x + x * 4x))
-24 + 20x + -4x2 = (-9 + -3x + (12x + 4x2))

Combine like terms: -3x + 12x = 9x
-24 + 20x + -4x2 = (-9 + 9x + 4x2)

Solving
-24 + 20x + -4x2 = -9 + 9x + 4x2

Solving for variable 'x'.

Reorder the terms:
-24 + 9 + 20x + -9x + -4x2 + -4x2 = -9 + 9x + 4x2 + 9 + -9x + -4x2

Combine like terms: -24 + 9 = -15
-15 + 20x + -9x + -4x2 + -4x2 = -9 + 9x + 4x2 + 9 + -9x + -4x2

Combine like terms: 20x + -9x = 11x
-15 + 11x + -4x2 + -4x2 = -9 + 9x + 4x2 + 9 + -9x + -4x2

Combine like terms: -4x2 + -4x2 = -8x2
-15 + 11x + -8x2 = -9 + 9x + 4x2 + 9 + -9x + -4x2

Reorder the terms:
-15 + 11x + -8x2 = -9 + 9 + 9x + -9x + 4x2 + -4x2

Combine like terms: -9 + 9 = 0
-15 + 11x + -8x2 = 0 + 9x + -9x + 4x2 + -4x2
-15 + 11x + -8x2 = 9x + -9x + 4x2 + -4x2

Combine like terms: 9x + -9x = 0
-15 + 11x + -8x2 = 0 + 4x2 + -4x2
-15 + 11x + -8x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15 + 11x + -8x2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
1.875 + -1.375x + x2 = 0

Move the constant term to the right:

Add '-1.875' to each side of the equation.
1.875 + -1.375x + -1.875 + x2 = 0 + -1.875

Reorder the terms:
1.875 + -1.875 + -1.375x + x2 = 0 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + -1.375x + x2 = 0 + -1.875
-1.375x + x2 = 0 + -1.875

Combine like terms: 0 + -1.875 = -1.875
-1.375x + x2 = -1.875

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = -1.875 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = -1.875 + 0.47265625

Combine like terms: -1.875 + 0.47265625 = -1.40234375
0.47265625 + -1.375x + x2 = -1.40234375

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = -1.40234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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