y^2-6y+3=0

Solution for y^2-6y+3=0 equation:

Simplifying
y2 + -6y + 3 = 0

Reorder the terms:
3 + -6y + y2 = 0

Solving
3 + -6y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -6y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -6y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -6y + y2 = 0 + -3
-6y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
-6y + y2 = -3

The y term is -6y.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6y + 9 + y2 = -3 + 9

Reorder the terms:
9 + -6y + y2 = -3 + 9

Combine like terms: -3 + 9 = 6
9 + -6y + y2 = 6

Factor a perfect square on the left side:
(y + -3)(y + -3) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(y + -3) equal to 2.449489743 and -2.449489743.

Subproblem 1
y + -3 = 2.449489743

Simplifying
y + -3 = 2.449489743

Reorder the terms:
-3 + y = 2.449489743

Solving
-3 + y = 2.449489743

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = 2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + y = 2.449489743 + 3
y = 2.449489743 + 3

Combine like terms: 2.449489743 + 3 = 5.449489743
y = 5.449489743

Simplifying
y = 5.449489743

Subproblem 2
y + -3 = -2.449489743

Simplifying
y + -3 = -2.449489743

Reorder the terms:
-3 + y = -2.449489743

Solving
-3 + y = -2.449489743

Solving for variable 'y'.

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

Add '3' to each side of the equation.
-3 + 3 + y = -2.449489743 + 3

Combine like terms: -3 + 3 = 0
0 + y = -2.449489743 + 3
y = -2.449489743 + 3

Combine like terms: -2.449489743 + 3 = 0.550510257
y = 0.550510257

Simplifying
y = 0.550510257

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.449489743, 0.550510257}