6(4-t)(-4+4t)=15

Solution for 6(4-t)(-4+4t)=15 equation:

Simplifying
6(4 + -1t)(-4 + 4t) = 15

Multiply (4 + -1t) * (-4 + 4t)
6(4(-4 + 4t) + -1t * (-4 + 4t)) = 15
6((-4 * 4 + 4t * 4) + -1t * (-4 + 4t)) = 15
6((-16 + 16t) + -1t * (-4 + 4t)) = 15
6(-16 + 16t + (-4 * -1t + 4t * -1t)) = 15
6(-16 + 16t + (4t + -4t2)) = 15

Combine like terms: 16t + 4t = 20t
6(-16 + 20t + -4t2) = 15
(-16 * 6 + 20t * 6 + -4t2 * 6) = 15
(-96 + 120t + -24t2) = 15

Solving
-96 + 120t + -24t2 = 15

Solving for variable 't'.

Reorder the terms:
-96 + -15 + 120t + -24t2 = 15 + -15

Combine like terms: -96 + -15 = -111
-111 + 120t + -24t2 = 15 + -15

Combine like terms: 15 + -15 = 0
-111 + 120t + -24t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-37 + 40t + -8t2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-37 + 40t + -8t2)' equal to zero and attempt to solve:

Simplifying
-37 + 40t + -8t2 = 0

Solving
-37 + 40t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
4.625 + -5t + t2 = 0

Move the constant term to the right:

Add '-4.625' to each side of the equation.
4.625 + -5t + -4.625 + t2 = 0 + -4.625

Reorder the terms:
4.625 + -4.625 + -5t + t2 = 0 + -4.625

Combine like terms: 4.625 + -4.625 = 0.000
0.000 + -5t + t2 = 0 + -4.625
-5t + t2 = 0 + -4.625

Combine like terms: 0 + -4.625 = -4.625
-5t + t2 = -4.625

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -4.625 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -4.625 + 6.25

Combine like terms: -4.625 + 6.25 = 1.625
6.25 + -5t + t2 = 1.625

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 1.625

Calculate the square root of the right side: 1.274754878

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.274754878 and -1.274754878.

Subproblem 1
t + -2.5 = 1.274754878

Simplifying
t + -2.5 = 1.274754878

Reorder the terms:
-2.5 + t = 1.274754878

Solving
-2.5 + t = 1.274754878

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 1.274754878 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.274754878 + 2.5
t = 1.274754878 + 2.5

Combine like terms: 1.274754878 + 2.5 = 3.774754878
t = 3.774754878

Simplifying
t = 3.774754878

Subproblem 2
t + -2.5 = -1.274754878

Simplifying
t + -2.5 = -1.274754878

Reorder the terms:
-2.5 + t = -1.274754878

Solving
-2.5 + t = -1.274754878

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -1.274754878 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.274754878 + 2.5
t = -1.274754878 + 2.5

Combine like terms: -1.274754878 + 2.5 = 1.225245122
t = 1.225245122

Simplifying
t = 1.225245122

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.774754878, 1.225245122}
Solution
t = {3.774754878, 1.225245122}