3(2t-1)2t=6-t

Solution for 3(2t-1)2t=6-t equation:

Simplifying
3(2t + -1) * 2t = 6 + -1t

Reorder the terms:
3(-1 + 2t) * 2t = 6 + -1t

Reorder the terms for easier multiplication:
3 * 2t(-1 + 2t) = 6 + -1t

Multiply 3 * 2
6t(-1 + 2t) = 6 + -1t
(-1 * 6t + 2t * 6t) = 6 + -1t
(-6t + 12t2) = 6 + -1t

Solving
-6t + 12t2 = 6 + -1t

Solving for variable 't'.

Reorder the terms:
-6 + -6t + t + 12t2 = 6 + -1t + -6 + t

Combine like terms: -6t + t = -5t
-6 + -5t + 12t2 = 6 + -1t + -6 + t

Reorder the terms:
-6 + -5t + 12t2 = 6 + -6 + -1t + t

Combine like terms: 6 + -6 = 0
-6 + -5t + 12t2 = 0 + -1t + t
-6 + -5t + 12t2 = -1t + t

Combine like terms: -1t + t = 0
-6 + -5t + 12t2 = 0

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

Divide each side by '12'.
-0.5 + -0.4166666667t + t2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.4166666667t + 0.5 + t2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.4166666667t + t2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.4166666667t + t2 = 0 + 0.5
-0.4166666667t + t2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.4166666667t + t2 = 0.5

The t term is -0.4166666667t.  Take half its coefficient (-0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
-0.4166666667t + 0.04340277781 + t2 = 0.5 + 0.04340277781

Reorder the terms:
0.04340277781 + -0.4166666667t + t2 = 0.5 + 0.04340277781

Combine like terms: 0.5 + 0.04340277781 = 0.54340277781
0.04340277781 + -0.4166666667t + t2 = 0.54340277781

Factor a perfect square on the left side:
(t + -0.2083333334)(t + -0.2083333334) = 0.54340277781

Calculate the square root of the right side: 0.737158584

Break this problem into two subproblems by setting 
(t + -0.2083333334) equal to 0.737158584 and -0.737158584.

Subproblem 1
t + -0.2083333334 = 0.737158584

Simplifying
t + -0.2083333334 = 0.737158584

Reorder the terms:
-0.2083333334 + t = 0.737158584

Solving
-0.2083333334 + t = 0.737158584

Solving for variable 't'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + t = 0.737158584 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + t = 0.737158584 + 0.2083333334
t = 0.737158584 + 0.2083333334

Combine like terms: 0.737158584 + 0.2083333334 = 0.9454919174
t = 0.9454919174

Simplifying
t = 0.9454919174

Subproblem 2
t + -0.2083333334 = -0.737158584

Simplifying
t + -0.2083333334 = -0.737158584

Reorder the terms:
-0.2083333334 + t = -0.737158584

Solving
-0.2083333334 + t = -0.737158584

Solving for variable 't'.

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

Add '0.2083333334' to each side of the equation.
-0.2083333334 + 0.2083333334 + t = -0.737158584 + 0.2083333334

Combine like terms: -0.2083333334 + 0.2083333334 = 0.0000000000
0.0000000000 + t = -0.737158584 + 0.2083333334
t = -0.737158584 + 0.2083333334

Combine like terms: -0.737158584 + 0.2083333334 = -0.5288252506
t = -0.5288252506

Simplifying
t = -0.5288252506

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.9454919174, -0.5288252506}