-4(3t+8)t=6

Solution for -4(3t+8)t=6 equation:

Simplifying
-4(3t + 8) * t = 6

Reorder the terms:
-4(8 + 3t) * t = 6

Reorder the terms for easier multiplication:
-4t(8 + 3t) = 6
(8 * -4t + 3t * -4t) = 6
(-32t + -12t2) = 6

Solving
-32t + -12t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + -32t + -12t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -32t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 16t + 6t2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 16t + 6t2)' equal to zero and attempt to solve:

Simplifying
3 + 16t + 6t2 = 0

Solving
3 + 16t + 6t2 = 0

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

Divide each side by '6'.
0.5 + 2.666666667t + t2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.666666667t + -0.5 + t2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.666666667t + t2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.666666667t + t2 = 0 + -0.5
2.666666667t + t2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.666666667t + t2 = -0.5

The t term is 2.666666667t.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667t + 1.777777780 + t2 = -0.5 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667t + t2 = -0.5 + 1.777777780

Combine like terms: -0.5 + 1.777777780 = 1.27777778
1.777777780 + 2.666666667t + t2 = 1.27777778

Factor a perfect square on the left side:
(t + 1.333333334)(t + 1.333333334) = 1.27777778

Calculate the square root of the right side: 1.130388332

Break this problem into two subproblems by setting 
(t + 1.333333334) equal to 1.130388332 and -1.130388332.

Subproblem 1
t + 1.333333334 = 1.130388332

Simplifying
t + 1.333333334 = 1.130388332

Reorder the terms:
1.333333334 + t = 1.130388332

Solving
1.333333334 + t = 1.130388332

Solving for variable 't'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + t = 1.130388332 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + t = 1.130388332 + -1.333333334
t = 1.130388332 + -1.333333334

Combine like terms: 1.130388332 + -1.333333334 = -0.202945002
t = -0.202945002

Simplifying
t = -0.202945002

Subproblem 2
t + 1.333333334 = -1.130388332

Simplifying
t + 1.333333334 = -1.130388332

Reorder the terms:
1.333333334 + t = -1.130388332

Solving
1.333333334 + t = -1.130388332

Solving for variable 't'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + t = -1.130388332 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + t = -1.130388332 + -1.333333334
t = -1.130388332 + -1.333333334

Combine like terms: -1.130388332 + -1.333333334 = -2.463721666
t = -2.463721666

Simplifying
t = -2.463721666

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.202945002, -2.463721666}
Solution
t = {-0.202945002, -2.463721666}