6x-4(x-2)=7x(3x-4)+19

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Solution for 6x-4(x-2)=7x(3x-4)+19 equation:


Simplifying
6x + -4(x + -2) = 7x(3x + -4) + 19

Reorder the terms:
6x + -4(-2 + x) = 7x(3x + -4) + 19
6x + (-2 * -4 + x * -4) = 7x(3x + -4) + 19
6x + (8 + -4x) = 7x(3x + -4) + 19

Reorder the terms:
8 + 6x + -4x = 7x(3x + -4) + 19

Combine like terms: 6x + -4x = 2x
8 + 2x = 7x(3x + -4) + 19

Reorder the terms:
8 + 2x = 7x(-4 + 3x) + 19
8 + 2x = (-4 * 7x + 3x * 7x) + 19
8 + 2x = (-28x + 21x2) + 19

Reorder the terms:
8 + 2x = 19 + -28x + 21x2

Solving
8 + 2x = 19 + -28x + 21x2

Solving for variable 'x'.

Reorder the terms:
8 + -19 + 2x + 28x + -21x2 = 19 + -28x + 21x2 + -19 + 28x + -21x2

Combine like terms: 8 + -19 = -11
-11 + 2x + 28x + -21x2 = 19 + -28x + 21x2 + -19 + 28x + -21x2

Combine like terms: 2x + 28x = 30x
-11 + 30x + -21x2 = 19 + -28x + 21x2 + -19 + 28x + -21x2

Reorder the terms:
-11 + 30x + -21x2 = 19 + -19 + -28x + 28x + 21x2 + -21x2

Combine like terms: 19 + -19 = 0
-11 + 30x + -21x2 = 0 + -28x + 28x + 21x2 + -21x2
-11 + 30x + -21x2 = -28x + 28x + 21x2 + -21x2

Combine like terms: -28x + 28x = 0
-11 + 30x + -21x2 = 0 + 21x2 + -21x2
-11 + 30x + -21x2 = 21x2 + -21x2

Combine like terms: 21x2 + -21x2 = 0
-11 + 30x + -21x2 = 0

Begin completing the square.  Divide all terms by
-21 the coefficient of the squared term: 

Divide each side by '-21'.
0.5238095238 + -1.428571429x + x2 = 0

Move the constant term to the right:

Add '-0.5238095238' to each side of the equation.
0.5238095238 + -1.428571429x + -0.5238095238 + x2 = 0 + -0.5238095238

Reorder the terms:
0.5238095238 + -0.5238095238 + -1.428571429x + x2 = 0 + -0.5238095238

Combine like terms: 0.5238095238 + -0.5238095238 = 0.0000000000
0.0000000000 + -1.428571429x + x2 = 0 + -0.5238095238
-1.428571429x + x2 = 0 + -0.5238095238

Combine like terms: 0 + -0.5238095238 = -0.5238095238
-1.428571429x + x2 = -0.5238095238

The x term is -1.428571429x.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429x + 0.5102040819 + x2 = -0.5238095238 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429x + x2 = -0.5238095238 + 0.5102040819

Combine like terms: -0.5238095238 + 0.5102040819 = -0.0136054419
0.5102040819 + -1.428571429x + x2 = -0.0136054419

Factor a perfect square on the left side:
(x + -0.7142857145)(x + -0.7142857145) = -0.0136054419

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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