6t^2-48t+8=0

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Solution for 6t^2-48t+8=0 equation: 


Simplifying
6t2 + -48t + 8 = 0

Reorder the terms:
8 + -48t + 6t2 = 0

Solving
8 + -48t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -24t + 3t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -24t + 3t2)' equal to zero and attempt to solve:

Simplifying
4 + -24t + 3t2 = 0

Solving
4 + -24t + 3t2 = 0

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

Divide each side by '3'.
1.333333333 + -8t + t2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -8t + -1.333333333 + t2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -8t + t2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -8t + t2 = 0 + -1.333333333
-8t + t2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-8t + t2 = -1.333333333

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = -1.333333333 + 16

Reorder the terms:
16 + -8t + t2 = -1.333333333 + 16

Combine like terms: -1.333333333 + 16 = 14.666666667
16 + -8t + t2 = 14.666666667

Factor a perfect square on the left side:
(t + -4)(t + -4) = 14.666666667

Calculate the square root of the right side: 3.829708431

Break this problem into two subproblems by setting 
(t + -4) equal to 3.829708431 and -3.829708431.


Subproblem 1
t + -4 = 3.829708431

Simplifying
t + -4 = 3.829708431

Reorder the terms:
-4 + t = 3.829708431

Solving
-4 + t = 3.829708431

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = 3.829708431 + 4

Combine like terms: -4 + 4 = 0
0 + t = 3.829708431 + 4
t = 3.829708431 + 4

Combine like terms: 3.829708431 + 4 = 7.829708431
t = 7.829708431

Simplifying
t = 7.829708431


Subproblem 2
t + -4 = -3.829708431

Simplifying
t + -4 = -3.829708431

Reorder the terms:
-4 + t = -3.829708431

Solving
-4 + t = -3.829708431

Solving for variable 't'.

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

Add '4' to each side of the equation.
-4 + 4 + t = -3.829708431 + 4

Combine like terms: -4 + 4 = 0
0 + t = -3.829708431 + 4
t = -3.829708431 + 4

Combine like terms: -3.829708431 + 4 = 0.170291569
t = 0.170291569

Simplifying
t = 0.170291569


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.829708431, 0.170291569}
Solution
t = {7.829708431, 0.170291569}

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