-6=3x^2-4x+1

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Solution for -6=3x^2-4x+1 equation: 


Simplifying
-6 = 3x2 + -4x + 1

Reorder the terms:
-6 = 1 + -4x + 3x2

Solving
-6 = 1 + -4x + 3x2

Solving for variable 'x'.

Combine like terms: -6 + -1 = -7
-7 + 4x + -3x2 = 1 + -4x + 3x2 + -1 + 4x + -3x2

Reorder the terms:
-7 + 4x + -3x2 = 1 + -1 + -4x + 4x + 3x2 + -3x2

Combine like terms: 1 + -1 = 0
-7 + 4x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2
-7 + 4x + -3x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-7 + 4x + -3x2 = 0 + 3x2 + -3x2
-7 + 4x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-7 + 4x + -3x2 = 0

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

Divide each side by '-3'.
2.333333333 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -1.333333333x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -1.333333333x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -2.333333333
-1.333333333x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-1.333333333x + x2 = -2.333333333

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -2.333333333 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -2.333333333 + 0.4444444442

Combine like terms: -2.333333333 + 0.4444444442 = -1.8888888888
0.4444444442 + -1.333333333x + x2 = -1.8888888888

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -1.8888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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