-3(t+5)(4t+2)=8

Solution for -3(t+5)(4t+2)=8 equation:

Simplifying
-3(t + 5)(4t + 2) = 8

Reorder the terms:
-3(5 + t)(4t + 2) = 8

Reorder the terms:
-3(5 + t)(2 + 4t) = 8

Multiply (5 + t) * (2 + 4t)
-3(5(2 + 4t) + t(2 + 4t)) = 8
-3((2 * 5 + 4t * 5) + t(2 + 4t)) = 8
-3((10 + 20t) + t(2 + 4t)) = 8
-3(10 + 20t + (2 * t + 4t * t)) = 8
-3(10 + 20t + (2t + 4t2)) = 8

Combine like terms: 20t + 2t = 22t
-3(10 + 22t + 4t2) = 8
(10 * -3 + 22t * -3 + 4t2 * -3) = 8
(-30 + -66t + -12t2) = 8

Solving
-30 + -66t + -12t2 = 8

Solving for variable 't'.

Reorder the terms:
-30 + -8 + -66t + -12t2 = 8 + -8

Combine like terms: -30 + -8 = -38
-38 + -66t + -12t2 = 8 + -8

Combine like terms: 8 + -8 = 0
-38 + -66t + -12t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(19 + 33t + 6t2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(19 + 33t + 6t2)' equal to zero and attempt to solve:

Simplifying
19 + 33t + 6t2 = 0

Solving
19 + 33t + 6t2 = 0

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

Divide each side by '6'.
3.166666667 + 5.5t + t2 = 0

Move the constant term to the right:

Add '-3.166666667' to each side of the equation.
3.166666667 + 5.5t + -3.166666667 + t2 = 0 + -3.166666667

Reorder the terms:
3.166666667 + -3.166666667 + 5.5t + t2 = 0 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + 5.5t + t2 = 0 + -3.166666667
5.5t + t2 = 0 + -3.166666667

Combine like terms: 0 + -3.166666667 = -3.166666667
5.5t + t2 = -3.166666667

The t term is 5.5t.  Take half its coefficient (2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
5.5t + 7.5625 + t2 = -3.166666667 + 7.5625

Reorder the terms:
7.5625 + 5.5t + t2 = -3.166666667 + 7.5625

Combine like terms: -3.166666667 + 7.5625 = 4.395833333
7.5625 + 5.5t + t2 = 4.395833333

Factor a perfect square on the left side:
(t + 2.75)(t + 2.75) = 4.395833333

Calculate the square root of the right side: 2.096624271

Break this problem into two subproblems by setting 
(t + 2.75) equal to 2.096624271 and -2.096624271.

Subproblem 1
t + 2.75 = 2.096624271

Simplifying
t + 2.75 = 2.096624271

Reorder the terms:
2.75 + t = 2.096624271

Solving
2.75 + t = 2.096624271

Solving for variable 't'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + t = 2.096624271 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + t = 2.096624271 + -2.75
t = 2.096624271 + -2.75

Combine like terms: 2.096624271 + -2.75 = -0.653375729
t = -0.653375729

Simplifying
t = -0.653375729

Subproblem 2
t + 2.75 = -2.096624271

Simplifying
t + 2.75 = -2.096624271

Reorder the terms:
2.75 + t = -2.096624271

Solving
2.75 + t = -2.096624271

Solving for variable 't'.

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

Add '-2.75' to each side of the equation.
2.75 + -2.75 + t = -2.096624271 + -2.75

Combine like terms: 2.75 + -2.75 = 0.00
0.00 + t = -2.096624271 + -2.75
t = -2.096624271 + -2.75

Combine like terms: -2.096624271 + -2.75 = -4.846624271
t = -4.846624271

Simplifying
t = -4.846624271

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.653375729, -4.846624271}
Solution
t = {-0.653375729, -4.846624271}