t=t^2-4t+3

Solution for t=t^2-4t+3 equation:

Simplifying
t = t2 + -4t + 3

Reorder the terms:
t = 3 + -4t + t2

Solving
t = 3 + -4t + t2

Solving for variable 't'.

Reorder the terms:
-3 + t + 4t + -1t2 = 3 + -4t + t2 + -3 + 4t + -1t2

Combine like terms: t + 4t = 5t
-3 + 5t + -1t2 = 3 + -4t + t2 + -3 + 4t + -1t2

Reorder the terms:
-3 + 5t + -1t2 = 3 + -3 + -4t + 4t + t2 + -1t2

Combine like terms: 3 + -3 = 0
-3 + 5t + -1t2 = 0 + -4t + 4t + t2 + -1t2
-3 + 5t + -1t2 = -4t + 4t + t2 + -1t2

Combine like terms: -4t + 4t = 0
-3 + 5t + -1t2 = 0 + t2 + -1t2
-3 + 5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-3 + 5t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -5t + t2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -5t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -5t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5t + t2 = 0 + -3
-5t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-5t + t2 = -3

The t term is -5t.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5t + 6.25 + t2 = -3 + 6.25

Reorder the terms:
6.25 + -5t + t2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + -5t + t2 = 3.25

Factor a perfect square on the left side:
(t + -2.5)(t + -2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(t + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
t + -2.5 = 1.802775638

Simplifying
t + -2.5 = 1.802775638

Reorder the terms:
-2.5 + t = 1.802775638

Solving
-2.5 + t = 1.802775638

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = 1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = 1.802775638 + 2.5
t = 1.802775638 + 2.5

Combine like terms: 1.802775638 + 2.5 = 4.302775638
t = 4.302775638

Simplifying
t = 4.302775638

Subproblem 2
t + -2.5 = -1.802775638

Simplifying
t + -2.5 = -1.802775638

Reorder the terms:
-2.5 + t = -1.802775638

Solving
-2.5 + t = -1.802775638

Solving for variable 't'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + t = -1.802775638 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + t = -1.802775638 + 2.5
t = -1.802775638 + 2.5

Combine like terms: -1.802775638 + 2.5 = 0.697224362
t = 0.697224362

Simplifying
t = 0.697224362

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.302775638, 0.697224362}