(-2y^2-6y)+(4y^2-1)=

Solution for (-2y^2-6y)+(4y^2-1)= equation:

Simplifying
(-2y2 + -6y) + (4y2 + -1) = 0

Reorder the terms:
(-6y + -2y2) + (4y2 + -1) = 0

Remove parenthesis around (-6y + -2y2)
-6y + -2y2 + (4y2 + -1) = 0

Reorder the terms:
-6y + -2y2 + (-1 + 4y2) = 0

Remove parenthesis around (-1 + 4y2)
-6y + -2y2 + -1 + 4y2 = 0

Reorder the terms:
-1 + -6y + -2y2 + 4y2 = 0

Combine like terms: -2y2 + 4y2 = 2y2
-1 + -6y + 2y2 = 0

Solving
-1 + -6y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-0.5 + -3y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3y + y2 = 0 + 0.5
-3y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3y + y2 = 0.5

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 0.5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 0.5 + 2.25

Combine like terms: 0.5 + 2.25 = 2.75
2.25 + -3y + y2 = 2.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
y + -1.5 = 1.658312395

Simplifying
y + -1.5 = 1.658312395

Reorder the terms:
-1.5 + y = 1.658312395

Solving
-1.5 + y = 1.658312395

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.658312395 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.658312395 + 1.5
y = 1.658312395 + 1.5

Combine like terms: 1.658312395 + 1.5 = 3.158312395
y = 3.158312395

Simplifying
y = 3.158312395

Subproblem 2
y + -1.5 = -1.658312395

Simplifying
y + -1.5 = -1.658312395

Reorder the terms:
-1.5 + y = -1.658312395

Solving
-1.5 + y = -1.658312395

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.658312395 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.658312395 + 1.5
y = -1.658312395 + 1.5

Combine like terms: -1.658312395 + 1.5 = -0.158312395
y = -0.158312395

Simplifying
y = -0.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.158312395, -0.158312395}