2x(3x+1)=4(x-1)

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Solution for 2x(3x+1)=4(x-1) equation: 


Simplifying
2x(3x + 1) = 4(x + -1)

Reorder the terms:
2x(1 + 3x) = 4(x + -1)
(1 * 2x + 3x * 2x) = 4(x + -1)
(2x + 6x2) = 4(x + -1)

Reorder the terms:
2x + 6x2 = 4(-1 + x)
2x + 6x2 = (-1 * 4 + x * 4)
2x + 6x2 = (-4 + 4x)

Solving
2x + 6x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
4 + 2x + -4x + 6x2 = -4 + 4x + 4 + -4x

Combine like terms: 2x + -4x = -2x
4 + -2x + 6x2 = -4 + 4x + 4 + -4x

Reorder the terms:
4 + -2x + 6x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
4 + -2x + 6x2 = 0 + 4x + -4x
4 + -2x + 6x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
4 + -2x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -1x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + -1x + 3x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x + 3x2 = 0

Solving
2 + -1x + 3x2 = 0

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

Divide each side by '3'.
0.6666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -0.3333333333x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -0.3333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -0.3333333333x + x2 = 0 + -0.6666666667
-0.3333333333x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-0.3333333333x + x2 = -0.6666666667

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = -0.6666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = -0.6666666667 + 0.02777777779

Combine like terms: -0.6666666667 + 0.02777777779 = -0.63888888891
0.02777777779 + -0.3333333333x + x2 = -0.63888888891

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = -0.63888888891

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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