9(t+5+3)4t+6=20(t+2+10)

Solution for 9(t+5+3)4t+6=20(t+2+10) equation:

Simplifying
9(t + 5 + 3) * 4t + 6 = 20(t + 2 + 10)

Reorder the terms:
9(5 + 3 + t) * 4t + 6 = 20(t + 2 + 10)

Combine like terms: 5 + 3 = 8
9(8 + t) * 4t + 6 = 20(t + 2 + 10)

Reorder the terms for easier multiplication:
9 * 4t(8 + t) + 6 = 20(t + 2 + 10)

Multiply 9 * 4
36t(8 + t) + 6 = 20(t + 2 + 10)
(8 * 36t + t * 36t) + 6 = 20(t + 2 + 10)
(288t + 36t2) + 6 = 20(t + 2 + 10)

Reorder the terms:
6 + 288t + 36t2 = 20(t + 2 + 10)

Reorder the terms:
6 + 288t + 36t2 = 20(2 + 10 + t)

Combine like terms: 2 + 10 = 12
6 + 288t + 36t2 = 20(12 + t)
6 + 288t + 36t2 = (12 * 20 + t * 20)
6 + 288t + 36t2 = (240 + 20t)

Solving
6 + 288t + 36t2 = 240 + 20t

Solving for variable 't'.

Reorder the terms:
6 + -240 + 288t + -20t + 36t2 = 240 + 20t + -240 + -20t

Combine like terms: 6 + -240 = -234
-234 + 288t + -20t + 36t2 = 240 + 20t + -240 + -20t

Combine like terms: 288t + -20t = 268t
-234 + 268t + 36t2 = 240 + 20t + -240 + -20t

Reorder the terms:
-234 + 268t + 36t2 = 240 + -240 + 20t + -20t

Combine like terms: 240 + -240 = 0
-234 + 268t + 36t2 = 0 + 20t + -20t
-234 + 268t + 36t2 = 20t + -20t

Combine like terms: 20t + -20t = 0
-234 + 268t + 36t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-117 + 134t + 18t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-117 + 134t + 18t2)' equal to zero and attempt to solve:

Simplifying
-117 + 134t + 18t2 = 0

Solving
-117 + 134t + 18t2 = 0

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

Divide each side by '18'.
-6.5 + 7.444444444t + t2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 7.444444444t + 6.5 + t2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 7.444444444t + t2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 7.444444444t + t2 = 0 + 6.5
7.444444444t + t2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
7.444444444t + t2 = 6.5

The t term is 7.444444444t.  Take half its coefficient (3.722222222).
Square it (13.85493827) and add it to both sides.

Add '13.85493827' to each side of the equation.
7.444444444t + 13.85493827 + t2 = 6.5 + 13.85493827

Reorder the terms:
13.85493827 + 7.444444444t + t2 = 6.5 + 13.85493827

Combine like terms: 6.5 + 13.85493827 = 20.35493827
13.85493827 + 7.444444444t + t2 = 20.35493827

Factor a perfect square on the left side:
(t + 3.722222222)(t + 3.722222222) = 20.35493827

Calculate the square root of the right side: 4.511644741

Break this problem into two subproblems by setting 
(t + 3.722222222) equal to 4.511644741 and -4.511644741.

Subproblem 1
t + 3.722222222 = 4.511644741

Simplifying
t + 3.722222222 = 4.511644741

Reorder the terms:
3.722222222 + t = 4.511644741

Solving
3.722222222 + t = 4.511644741

Solving for variable 't'.

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

Add '-3.722222222' to each side of the equation.
3.722222222 + -3.722222222 + t = 4.511644741 + -3.722222222

Combine like terms: 3.722222222 + -3.722222222 = 0.000000000
0.000000000 + t = 4.511644741 + -3.722222222
t = 4.511644741 + -3.722222222

Combine like terms: 4.511644741 + -3.722222222 = 0.789422519
t = 0.789422519

Simplifying
t = 0.789422519

Subproblem 2
t + 3.722222222 = -4.511644741

Simplifying
t + 3.722222222 = -4.511644741

Reorder the terms:
3.722222222 + t = -4.511644741

Solving
3.722222222 + t = -4.511644741

Solving for variable 't'.

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

Add '-3.722222222' to each side of the equation.
3.722222222 + -3.722222222 + t = -4.511644741 + -3.722222222

Combine like terms: 3.722222222 + -3.722222222 = 0.000000000
0.000000000 + t = -4.511644741 + -3.722222222
t = -4.511644741 + -3.722222222

Combine like terms: -4.511644741 + -3.722222222 = -8.233866963
t = -8.233866963

Simplifying
t = -8.233866963

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.789422519, -8.233866963}
Solution
t = {0.789422519, -8.233866963}