(3x-2)4-4x(3x-2)=45

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Solution for (3x-2)4-4x(3x-2)=45 equation: 


Simplifying
(3x + -2) * 4 + -4x(3x + -2) = 45

Reorder the terms:
(-2 + 3x) * 4 + -4x(3x + -2) = 45

Reorder the terms for easier multiplication:
4(-2 + 3x) + -4x(3x + -2) = 45
(-2 * 4 + 3x * 4) + -4x(3x + -2) = 45
(-8 + 12x) + -4x(3x + -2) = 45

Reorder the terms:
-8 + 12x + -4x(-2 + 3x) = 45
-8 + 12x + (-2 * -4x + 3x * -4x) = 45
-8 + 12x + (8x + -12x2) = 45

Combine like terms: 12x + 8x = 20x
-8 + 20x + -12x2 = 45

Solving
-8 + 20x + -12x2 = 45

Solving for variable 'x'.

Reorder the terms:
-8 + -45 + 20x + -12x2 = 45 + -45

Combine like terms: -8 + -45 = -53
-53 + 20x + -12x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-53 + 20x + -12x2 = 0

Begin completing the square.  Divide all terms by
-12 the coefficient of the squared term: 

Divide each side by '-12'.
4.416666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.416666667' to each side of the equation.
4.416666667 + -1.666666667x + -4.416666667 + x2 = 0 + -4.416666667

Reorder the terms:
4.416666667 + -4.416666667 + -1.666666667x + x2 = 0 + -4.416666667

Combine like terms: 4.416666667 + -4.416666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + -4.416666667
-1.666666667x + x2 = 0 + -4.416666667

Combine like terms: 0 + -4.416666667 = -4.416666667
-1.666666667x + x2 = -4.416666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -4.416666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -4.416666667 + 0.6944444447

Combine like terms: -4.416666667 + 0.6944444447 = -3.7222222223
0.6944444447 + -1.666666667x + x2 = -3.7222222223

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -3.7222222223

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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