-6x^2+6x-8=0

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Solution for -6x^2+6x-8=0 equation: 


Simplifying
-6x2 + 6x + -8 = 0

Reorder the terms:
-8 + 6x + -6x2 = 0

Solving
-8 + 6x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 3x + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 3x + -3x2 = 0

Solving
-4 + 3x + -3x2 = 0

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

Divide each side by '-3'.
1.333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -1x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -1x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + -1.333333333
-1x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-1x + x2 = -1.333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -1.333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1.333333333 + 0.25

Combine like terms: -1.333333333 + 0.25 = -1.083333333
0.25 + -1x + x2 = -1.083333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.083333333

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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