13(t-2)5t=6(3t+3)-9

Solution for 13(t-2)5t=6(3t+3)-9 equation:

Simplifying
13(t + -2) * 5t = 6(3t + 3) + -9

Reorder the terms:
13(-2 + t) * 5t = 6(3t + 3) + -9

Reorder the terms for easier multiplication:
13 * 5t(-2 + t) = 6(3t + 3) + -9

Multiply 13 * 5
65t(-2 + t) = 6(3t + 3) + -9
(-2 * 65t + t * 65t) = 6(3t + 3) + -9
(-130t + 65t2) = 6(3t + 3) + -9

Reorder the terms:
-130t + 65t2 = 6(3 + 3t) + -9
-130t + 65t2 = (3 * 6 + 3t * 6) + -9
-130t + 65t2 = (18 + 18t) + -9

Reorder the terms:
-130t + 65t2 = 18 + -9 + 18t

Combine like terms: 18 + -9 = 9
-130t + 65t2 = 9 + 18t

Solving
-130t + 65t2 = 9 + 18t

Solving for variable 't'.

Reorder the terms:
-9 + -130t + -18t + 65t2 = 9 + 18t + -9 + -18t

Combine like terms: -130t + -18t = -148t
-9 + -148t + 65t2 = 9 + 18t + -9 + -18t

Reorder the terms:
-9 + -148t + 65t2 = 9 + -9 + 18t + -18t

Combine like terms: 9 + -9 = 0
-9 + -148t + 65t2 = 0 + 18t + -18t
-9 + -148t + 65t2 = 18t + -18t

Combine like terms: 18t + -18t = 0
-9 + -148t + 65t2 = 0

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

Divide each side by '65'.
-0.1384615385 + -2.276923077t + t2 = 0

Move the constant term to the right:

Add '0.1384615385' to each side of the equation.
-0.1384615385 + -2.276923077t + 0.1384615385 + t2 = 0 + 0.1384615385

Reorder the terms:
-0.1384615385 + 0.1384615385 + -2.276923077t + t2 = 0 + 0.1384615385

Combine like terms: -0.1384615385 + 0.1384615385 = 0.0000000000
0.0000000000 + -2.276923077t + t2 = 0 + 0.1384615385
-2.276923077t + t2 = 0 + 0.1384615385

Combine like terms: 0 + 0.1384615385 = 0.1384615385
-2.276923077t + t2 = 0.1384615385

The t term is -2.276923077t.  Take half its coefficient (-1.138461539).
Square it (1.296094676) and add it to both sides.

Add '1.296094676' to each side of the equation.
-2.276923077t + 1.296094676 + t2 = 0.1384615385 + 1.296094676

Reorder the terms:
1.296094676 + -2.276923077t + t2 = 0.1384615385 + 1.296094676

Combine like terms: 0.1384615385 + 1.296094676 = 1.4345562145
1.296094676 + -2.276923077t + t2 = 1.4345562145

Factor a perfect square on the left side:
(t + -1.138461539)(t + -1.138461539) = 1.4345562145

Calculate the square root of the right side: 1.197729608

Break this problem into two subproblems by setting 
(t + -1.138461539) equal to 1.197729608 and -1.197729608.

Subproblem 1
t + -1.138461539 = 1.197729608

Simplifying
t + -1.138461539 = 1.197729608

Reorder the terms:
-1.138461539 + t = 1.197729608

Solving
-1.138461539 + t = 1.197729608

Solving for variable 't'.

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

Add '1.138461539' to each side of the equation.
-1.138461539 + 1.138461539 + t = 1.197729608 + 1.138461539

Combine like terms: -1.138461539 + 1.138461539 = 0.000000000
0.000000000 + t = 1.197729608 + 1.138461539
t = 1.197729608 + 1.138461539

Combine like terms: 1.197729608 + 1.138461539 = 2.336191147
t = 2.336191147

Simplifying
t = 2.336191147

Subproblem 2
t + -1.138461539 = -1.197729608

Simplifying
t + -1.138461539 = -1.197729608

Reorder the terms:
-1.138461539 + t = -1.197729608

Solving
-1.138461539 + t = -1.197729608

Solving for variable 't'.

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

Add '1.138461539' to each side of the equation.
-1.138461539 + 1.138461539 + t = -1.197729608 + 1.138461539

Combine like terms: -1.138461539 + 1.138461539 = 0.000000000
0.000000000 + t = -1.197729608 + 1.138461539
t = -1.197729608 + 1.138461539

Combine like terms: -1.197729608 + 1.138461539 = -0.059268069
t = -0.059268069

Simplifying
t = -0.059268069

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.336191147, -0.059268069}