0=y^2+4y-6

Solution for 0=y^2+4y-6 equation:

Simplifying
0 = y2 + 4y + -6

Reorder the terms:
0 = -6 + 4y + y2

Solving
0 = -6 + 4y + y2

Solving for variable 'y'.

Combine like terms: 0 + 6 = 6
6 + -4y + -1y2 = -6 + 4y + y2 + 6 + -4y + -1y2

Reorder the terms:
6 + -4y + -1y2 = -6 + 6 + 4y + -4y + y2 + -1y2

Combine like terms: -6 + 6 = 0
6 + -4y + -1y2 = 0 + 4y + -4y + y2 + -1y2
6 + -4y + -1y2 = 4y + -4y + y2 + -1y2

Combine like terms: 4y + -4y = 0
6 + -4y + -1y2 = 0 + y2 + -1y2
6 + -4y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6 + -4y + -1y2 = 0

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

Divide each side by '-1'.
-6 + 4y + y2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 4y + 6 + y2 = 0 + 6

Reorder the terms:
-6 + 6 + 4y + y2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 4y + y2 = 0 + 6
4y + y2 = 0 + 6

Combine like terms: 0 + 6 = 6
4y + y2 = 6

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 6 + 4

Reorder the terms:
4 + 4y + y2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + 4y + y2 = 10

Factor a perfect square on the left side:
(y + 2)(y + 2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(y + 2) equal to 3.16227766 and -3.16227766.

Subproblem 1
y + 2 = 3.16227766

Simplifying
y + 2 = 3.16227766

Reorder the terms:
2 + y = 3.16227766

Solving
2 + y = 3.16227766

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + y = 3.16227766 + -2
y = 3.16227766 + -2

Combine like terms: 3.16227766 + -2 = 1.16227766
y = 1.16227766

Simplifying
y = 1.16227766

Subproblem 2
y + 2 = -3.16227766

Simplifying
y + 2 = -3.16227766

Reorder the terms:
2 + y = -3.16227766

Solving
2 + y = -3.16227766

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -3.16227766 + -2

Combine like terms: 2 + -2 = 0
0 + y = -3.16227766 + -2
y = -3.16227766 + -2

Combine like terms: -3.16227766 + -2 = -5.16227766
y = -5.16227766

Simplifying
y = -5.16227766

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.16227766, -5.16227766}