-6t^2+22t-8=0

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Solution for -6t^2+22t-8=0 equation: 


Simplifying
-6t2 + 22t + -8 = 0

Reorder the terms:
-8 + 22t + -6t2 = 0

Solving
-8 + 22t + -6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 11t + -3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 11t + -3t2)' equal to zero and attempt to solve:

Simplifying
-4 + 11t + -3t2 = 0

Solving
-4 + 11t + -3t2 = 0

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

Divide each side by '-3'.
1.333333333 + -3.666666667t + t2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -3.666666667t + -1.333333333 + t2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -3.666666667t + t2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -3.666666667t + t2 = 0 + -1.333333333
-3.666666667t + t2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-3.666666667t + t2 = -1.333333333

The t term is -3.666666667t.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667t + 3.361111114 + t2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667t + t2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + -3.666666667t + t2 = 2.027777781

Factor a perfect square on the left side:
(t + -1.833333334)(t + -1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(t + -1.833333334) equal to 1.424000625 and -1.424000625.


Subproblem 1
t + -1.833333334 = 1.424000625

Simplifying
t + -1.833333334 = 1.424000625

Reorder the terms:
-1.833333334 + t = 1.424000625

Solving
-1.833333334 + t = 1.424000625

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + t = 1.424000625 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + t = 1.424000625 + 1.833333334
t = 1.424000625 + 1.833333334

Combine like terms: 1.424000625 + 1.833333334 = 3.257333959
t = 3.257333959

Simplifying
t = 3.257333959


Subproblem 2
t + -1.833333334 = -1.424000625

Simplifying
t + -1.833333334 = -1.424000625

Reorder the terms:
-1.833333334 + t = -1.424000625

Solving
-1.833333334 + t = -1.424000625

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + t = -1.424000625 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + t = -1.424000625 + 1.833333334
t = -1.424000625 + 1.833333334

Combine like terms: -1.424000625 + 1.833333334 = 0.409332709
t = 0.409332709

Simplifying
t = 0.409332709


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.257333959, 0.409332709}
Solution
t = {3.257333959, 0.409332709}

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