3(t-5)-16t=12-2t(t-3)

Solution for 3(t-5)-16t=12-2t(t-3) equation:

Simplifying
3(t + -5) + -16t = 12 + -2t(t + -3)

Reorder the terms:
3(-5 + t) + -16t = 12 + -2t(t + -3)
(-5 * 3 + t * 3) + -16t = 12 + -2t(t + -3)
(-15 + 3t) + -16t = 12 + -2t(t + -3)

Combine like terms: 3t + -16t = -13t
-15 + -13t = 12 + -2t(t + -3)

Reorder the terms:
-15 + -13t = 12 + -2t(-3 + t)
-15 + -13t = 12 + (-3 * -2t + t * -2t)
-15 + -13t = 12 + (6t + -2t2)

Solving
-15 + -13t = 12 + 6t + -2t2

Solving for variable 't'.

Reorder the terms:
-15 + -12 + -13t + -6t + 2t2 = 12 + 6t + -2t2 + -12 + -6t + 2t2

Combine like terms: -15 + -12 = -27
-27 + -13t + -6t + 2t2 = 12 + 6t + -2t2 + -12 + -6t + 2t2

Combine like terms: -13t + -6t = -19t
-27 + -19t + 2t2 = 12 + 6t + -2t2 + -12 + -6t + 2t2

Reorder the terms:
-27 + -19t + 2t2 = 12 + -12 + 6t + -6t + -2t2 + 2t2

Combine like terms: 12 + -12 = 0
-27 + -19t + 2t2 = 0 + 6t + -6t + -2t2 + 2t2
-27 + -19t + 2t2 = 6t + -6t + -2t2 + 2t2

Combine like terms: 6t + -6t = 0
-27 + -19t + 2t2 = 0 + -2t2 + 2t2
-27 + -19t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
-27 + -19t + 2t2 = 0

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

Divide each side by '2'.
-13.5 + -9.5t + t2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + -9.5t + 13.5 + t2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + -9.5t + t2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + -9.5t + t2 = 0 + 13.5
-9.5t + t2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
-9.5t + t2 = 13.5

The t term is -9.5t.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5t + 22.5625 + t2 = 13.5 + 22.5625

Reorder the terms:
22.5625 + -9.5t + t2 = 13.5 + 22.5625

Combine like terms: 13.5 + 22.5625 = 36.0625
22.5625 + -9.5t + t2 = 36.0625

Factor a perfect square on the left side:
(t + -4.75)(t + -4.75) = 36.0625

Calculate the square root of the right side: 6.005206075

Break this problem into two subproblems by setting 
(t + -4.75) equal to 6.005206075 and -6.005206075.

Subproblem 1
t + -4.75 = 6.005206075

Simplifying
t + -4.75 = 6.005206075

Reorder the terms:
-4.75 + t = 6.005206075

Solving
-4.75 + t = 6.005206075

Solving for variable 't'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + t = 6.005206075 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + t = 6.005206075 + 4.75
t = 6.005206075 + 4.75

Combine like terms: 6.005206075 + 4.75 = 10.755206075
t = 10.755206075

Simplifying
t = 10.755206075

Subproblem 2
t + -4.75 = -6.005206075

Simplifying
t + -4.75 = -6.005206075

Reorder the terms:
-4.75 + t = -6.005206075

Solving
-4.75 + t = -6.005206075

Solving for variable 't'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + t = -6.005206075 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + t = -6.005206075 + 4.75
t = -6.005206075 + 4.75

Combine like terms: -6.005206075 + 4.75 = -1.255206075
t = -1.255206075

Simplifying
t = -1.255206075

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.755206075, -1.255206075}