6x^2-32x+80=0

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Solution for 6x^2-32x+80=0 equation: 


Simplifying
6x2 + -32x + 80 = 0

Reorder the terms:
80 + -32x + 6x2 = 0

Solving
80 + -32x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(40 + -16x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(40 + -16x + 3x2)' equal to zero and attempt to solve:

Simplifying
40 + -16x + 3x2 = 0

Solving
40 + -16x + 3x2 = 0

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

Divide each side by '3'.
13.33333333 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + -5.333333333x + -13.33333333 + x2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + -5.333333333x + x2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + -5.333333333x + x2 = 0 + -13.33333333
-5.333333333x + x2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
-5.333333333x + x2 = -13.33333333

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = -13.33333333 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = -13.33333333 + 7.111111113

Combine like terms: -13.33333333 + 7.111111113 = -6.222222217
7.111111113 + -5.333333333x + x2 = -6.222222217

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = -6.222222217

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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