-6t(2t+8)=-48

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Solution for -6t(2t+8)=-48 equation: 


Simplifying
-6t(2t + 8) = -48

Reorder the terms:
-6t(8 + 2t) = -48
(8 * -6t + 2t * -6t) = -48
(-48t + -12t2) = -48

Solving
-48t + -12t2 = -48

Solving for variable 't'.

Reorder the terms:
48 + -48t + -12t2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + -48t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(4 + -4t + -1t2) = 0

Ignore the factor 12.

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

Simplifying
4 + -4t + -1t2 = 0

Solving
4 + -4t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 4t + t2 = 0

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4t + t2 = 8

Factor a perfect square on the left side:
(t + 2)(t + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(t + 2) equal to 2.828427125 and -2.828427125.


Subproblem 1
t + 2 = 2.828427125

Simplifying
t + 2 = 2.828427125

Reorder the terms:
2 + t = 2.828427125

Solving
2 + t = 2.828427125

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 = 2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + t = 2.828427125 + -2
t = 2.828427125 + -2

Combine like terms: 2.828427125 + -2 = 0.828427125
t = 0.828427125

Simplifying
t = 0.828427125


Subproblem 2
t + 2 = -2.828427125

Simplifying
t + 2 = -2.828427125

Reorder the terms:
2 + t = -2.828427125

Solving
2 + t = -2.828427125

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 = -2.828427125 + -2

Combine like terms: 2 + -2 = 0
0 + t = -2.828427125 + -2
t = -2.828427125 + -2

Combine like terms: -2.828427125 + -2 = -4.828427125
t = -4.828427125

Simplifying
t = -4.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.828427125, -4.828427125}
Solution
t = {0.828427125, -4.828427125}

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