13t+(-12t)=12t(-12t)+3.14

Solution for 13t+(-12t)=12t(-12t)+3.14 equation:

Simplifying
13t + (-12t) = 12t(-12t) + 3.14

Combine like terms: 13t + (-12t) = 1t
1t = 12t(-12t) + 3.14

Remove parenthesis around (-12t)
1t = 12t * -12t + 3.14

Reorder the terms for easier multiplication:
1t = 12 * -12t * t + 3.14

Multiply 12 * -12
1t = -144t * t + 3.14

Multiply t * t
1t = -144t2 + 3.14

Reorder the terms:
1t = 3.14 + -144t2

Solving
1t = 3.14 + -144t2

Solving for variable 't'.

Reorder the terms:
-3.14 + 1t + 144t2 = 3.14 + -144t2 + -3.14 + 144t2

Reorder the terms:
-3.14 + 1t + 144t2 = 3.14 + -3.14 + -144t2 + 144t2

Combine like terms: 3.14 + -3.14 = 0.00
-3.14 + 1t + 144t2 = 0.00 + -144t2 + 144t2
-3.14 + 1t + 144t2 = -144t2 + 144t2

Combine like terms: -144t2 + 144t2 = 0
-3.14 + 1t + 144t2 = 0

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

Divide each side by '144'.
-0.02180555556 + 0.006944444444t + t2 = 0

Move the constant term to the right:

Add '0.02180555556' to each side of the equation.
-0.02180555556 + 0.006944444444t + 0.02180555556 + t2 = 0 + 0.02180555556

Reorder the terms:
-0.02180555556 + 0.02180555556 + 0.006944444444t + t2 = 0 + 0.02180555556

Combine like terms: -0.02180555556 + 0.02180555556 = 0.00000000000
0.00000000000 + 0.006944444444t + t2 = 0 + 0.02180555556
0.006944444444t + t2 = 0 + 0.02180555556

Combine like terms: 0 + 0.02180555556 = 0.02180555556
0.006944444444t + t2 = 0.02180555556

The t term is 0.006944444444t.  Take half its coefficient (0.003472222222).
Square it (0.00001205632716) and add it to both sides.

Add '0.00001205632716' to each side of the equation.
0.006944444444t + 0.00001205632716 + t2 = 0.02180555556 + 0.00001205632716

Reorder the terms:
0.00001205632716 + 0.006944444444t + t2 = 0.02180555556 + 0.00001205632716

Combine like terms: 0.02180555556 + 0.00001205632716 = 0.02181761188716
0.00001205632716 + 0.006944444444t + t2 = 0.02181761188716

Factor a perfect square on the left side:
(t + 0.003472222222)(t + 0.003472222222) = 0.02181761188716

Calculate the square root of the right side: 0.14770786

Break this problem into two subproblems by setting 
(t + 0.003472222222) equal to 0.14770786 and -0.14770786.

Subproblem 1
t + 0.003472222222 = 0.14770786

Simplifying
t + 0.003472222222 = 0.14770786

Reorder the terms:
0.003472222222 + t = 0.14770786

Solving
0.003472222222 + t = 0.14770786

Solving for variable 't'.

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

Add '-0.003472222222' to each side of the equation.
0.003472222222 + -0.003472222222 + t = 0.14770786 + -0.003472222222

Combine like terms: 0.003472222222 + -0.003472222222 = 0.000000000000
0.000000000000 + t = 0.14770786 + -0.003472222222
t = 0.14770786 + -0.003472222222

Combine like terms: 0.14770786 + -0.003472222222 = 0.144235637778
t = 0.144235637778

Simplifying
t = 0.144235637778

Subproblem 2
t + 0.003472222222 = -0.14770786

Simplifying
t + 0.003472222222 = -0.14770786

Reorder the terms:
0.003472222222 + t = -0.14770786

Solving
0.003472222222 + t = -0.14770786

Solving for variable 't'.

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

Add '-0.003472222222' to each side of the equation.
0.003472222222 + -0.003472222222 + t = -0.14770786 + -0.003472222222

Combine like terms: 0.003472222222 + -0.003472222222 = 0.000000000000
0.000000000000 + t = -0.14770786 + -0.003472222222
t = -0.14770786 + -0.003472222222

Combine like terms: -0.14770786 + -0.003472222222 = -0.151180082222
t = -0.151180082222

Simplifying
t = -0.151180082222

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.144235637778, -0.151180082222}