6t^2-4t+32=0

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Solution for 6t^2-4t+32=0 equation: 


Simplifying
6t2 + -4t + 32 = 0

Reorder the terms:
32 + -4t + 6t2 = 0

Solving
32 + -4t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -2t + 3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + -2t + 3t2)' equal to zero and attempt to solve:

Simplifying
16 + -2t + 3t2 = 0

Solving
16 + -2t + 3t2 = 0

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

Divide each side by '3'.
5.333333333 + -0.6666666667t + t2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -0.6666666667t + -5.333333333 + t2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -0.6666666667t + t2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -0.6666666667t + t2 = 0 + -5.333333333
-0.6666666667t + t2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-0.6666666667t + t2 = -5.333333333

The t term is -0.6666666667t.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667t + 0.1111111112 + t2 = -5.333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667t + t2 = -5.333333333 + 0.1111111112

Combine like terms: -5.333333333 + 0.1111111112 = -5.2222222218
0.1111111112 + -0.6666666667t + t2 = -5.2222222218

Factor a perfect square on the left side:
(t + -0.3333333334)(t + -0.3333333334) = -5.2222222218

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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