6t^2-24t+16=0

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Solution for 6t^2-24t+16=0 equation: 


Simplifying
6t2 + -24t + 16 = 0

Reorder the terms:
16 + -24t + 6t2 = 0

Solving
16 + -24t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -12t + 3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8 + -12t + 3t2)' equal to zero and attempt to solve:

Simplifying
8 + -12t + 3t2 = 0

Solving
8 + -12t + 3t2 = 0

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

Divide each side by '3'.
2.666666667 + -4t + t2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -4t + -2.666666667 + t2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -4t + t2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -4t + t2 = 0 + -2.666666667
-4t + t2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-4t + t2 = -2.666666667

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -2.666666667 + 4

Reorder the terms:
4 + -4t + t2 = -2.666666667 + 4

Combine like terms: -2.666666667 + 4 = 1.333333333
4 + -4t + t2 = 1.333333333

Factor a perfect square on the left side:
(t + -2)(t + -2) = 1.333333333

Calculate the square root of the right side: 1.154700538

Break this problem into two subproblems by setting 
(t + -2) equal to 1.154700538 and -1.154700538.


Subproblem 1
t + -2 = 1.154700538

Simplifying
t + -2 = 1.154700538

Reorder the terms:
-2 + t = 1.154700538

Solving
-2 + t = 1.154700538

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1.154700538 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.154700538 + 2
t = 1.154700538 + 2

Combine like terms: 1.154700538 + 2 = 3.154700538
t = 3.154700538

Simplifying
t = 3.154700538


Subproblem 2
t + -2 = -1.154700538

Simplifying
t + -2 = -1.154700538

Reorder the terms:
-2 + t = -1.154700538

Solving
-2 + t = -1.154700538

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1.154700538 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.154700538 + 2
t = -1.154700538 + 2

Combine like terms: -1.154700538 + 2 = 0.845299462
t = 0.845299462

Simplifying
t = 0.845299462


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.154700538, 0.845299462}
Solution
t = {3.154700538, 0.845299462}

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