t^2-12t+3=0

Solution for t^2-12t+3=0 equation:

Simplifying
t2 + -12t + 3 = 0

Reorder the terms:
3 + -12t + t2 = 0

Solving
3 + -12t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -12t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -12t + t2 = 0 + -3
-12t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12t + t2 = -3

The t term is -12t.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12t + 36 + t2 = -3 + 36

Reorder the terms:
36 + -12t + t2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + -12t + t2 = 33

Factor a perfect square on the left side:
(t + -6)(t + -6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(t + -6) equal to 5.744562647 and -5.744562647.

Subproblem 1
t + -6 = 5.744562647

Simplifying
t + -6 = 5.744562647

Reorder the terms:
-6 + t = 5.744562647

Solving
-6 + t = 5.744562647

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = 5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + t = 5.744562647 + 6
t = 5.744562647 + 6

Combine like terms: 5.744562647 + 6 = 11.744562647
t = 11.744562647

Simplifying
t = 11.744562647

Subproblem 2
t + -6 = -5.744562647

Simplifying
t + -6 = -5.744562647

Reorder the terms:
-6 + t = -5.744562647

Solving
-6 + t = -5.744562647

Solving for variable 't'.

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

Add '6' to each side of the equation.
-6 + 6 + t = -5.744562647 + 6

Combine like terms: -6 + 6 = 0
0 + t = -5.744562647 + 6
t = -5.744562647 + 6

Combine like terms: -5.744562647 + 6 = 0.255437353
t = 0.255437353

Simplifying
t = 0.255437353

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.744562647, 0.255437353}