11(t-6)4t=5(3t+4)-9

Solution for 11(t-6)4t=5(3t+4)-9 equation:

Simplifying
11(t + -6) * 4t = 5(3t + 4) + -9

Reorder the terms:
11(-6 + t) * 4t = 5(3t + 4) + -9

Reorder the terms for easier multiplication:
11 * 4t(-6 + t) = 5(3t + 4) + -9

Multiply 11 * 4
44t(-6 + t) = 5(3t + 4) + -9
(-6 * 44t + t * 44t) = 5(3t + 4) + -9
(-264t + 44t2) = 5(3t + 4) + -9

Reorder the terms:
-264t + 44t2 = 5(4 + 3t) + -9
-264t + 44t2 = (4 * 5 + 3t * 5) + -9
-264t + 44t2 = (20 + 15t) + -9

Reorder the terms:
-264t + 44t2 = 20 + -9 + 15t

Combine like terms: 20 + -9 = 11
-264t + 44t2 = 11 + 15t

Solving
-264t + 44t2 = 11 + 15t

Solving for variable 't'.

Reorder the terms:
-11 + -264t + -15t + 44t2 = 11 + 15t + -11 + -15t

Combine like terms: -264t + -15t = -279t
-11 + -279t + 44t2 = 11 + 15t + -11 + -15t

Reorder the terms:
-11 + -279t + 44t2 = 11 + -11 + 15t + -15t

Combine like terms: 11 + -11 = 0
-11 + -279t + 44t2 = 0 + 15t + -15t
-11 + -279t + 44t2 = 15t + -15t

Combine like terms: 15t + -15t = 0
-11 + -279t + 44t2 = 0

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

Divide each side by '44'.
-0.25 + -6.340909091t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -6.340909091t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -6.340909091t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -6.340909091t + t2 = 0 + 0.25
-6.340909091t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-6.340909091t + t2 = 0.25

The t term is -6.340909091t.  Take half its coefficient (-3.170454546).
Square it (10.05178203) and add it to both sides.

Add '10.05178203' to each side of the equation.
-6.340909091t + 10.05178203 + t2 = 0.25 + 10.05178203

Reorder the terms:
10.05178203 + -6.340909091t + t2 = 0.25 + 10.05178203

Combine like terms: 0.25 + 10.05178203 = 10.30178203
10.05178203 + -6.340909091t + t2 = 10.30178203

Factor a perfect square on the left side:
(t + -3.170454546)(t + -3.170454546) = 10.30178203

Calculate the square root of the right side: 3.209638925

Break this problem into two subproblems by setting 
(t + -3.170454546) equal to 3.209638925 and -3.209638925.

Subproblem 1
t + -3.170454546 = 3.209638925

Simplifying
t + -3.170454546 = 3.209638925

Reorder the terms:
-3.170454546 + t = 3.209638925

Solving
-3.170454546 + t = 3.209638925

Solving for variable 't'.

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

Add '3.170454546' to each side of the equation.
-3.170454546 + 3.170454546 + t = 3.209638925 + 3.170454546

Combine like terms: -3.170454546 + 3.170454546 = 0.000000000
0.000000000 + t = 3.209638925 + 3.170454546
t = 3.209638925 + 3.170454546

Combine like terms: 3.209638925 + 3.170454546 = 6.380093471
t = 6.380093471

Simplifying
t = 6.380093471

Subproblem 2
t + -3.170454546 = -3.209638925

Simplifying
t + -3.170454546 = -3.209638925

Reorder the terms:
-3.170454546 + t = -3.209638925

Solving
-3.170454546 + t = -3.209638925

Solving for variable 't'.

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

Add '3.170454546' to each side of the equation.
-3.170454546 + 3.170454546 + t = -3.209638925 + 3.170454546

Combine like terms: -3.170454546 + 3.170454546 = 0.000000000
0.000000000 + t = -3.209638925 + 3.170454546
t = -3.209638925 + 3.170454546

Combine like terms: -3.209638925 + 3.170454546 = -0.039184379
t = -0.039184379

Simplifying
t = -0.039184379

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.380093471, -0.039184379}