-4y^2-5=-10y

Solution for -4y^2-5=-10y equation:

Simplifying
-4y2 + -5 = -10y

Reorder the terms:
-5 + -4y2 = -10y

Solving
-5 + -4y2 = -10y

Solving for variable 'y'.

Reorder the terms:
-5 + 10y + -4y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
-5 + 10y + -4y2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
1.25 + -2.5y + y2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -2.5y + -1.25 + y2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -2.5y + y2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -2.5y + y2 = 0 + -1.25
-2.5y + y2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-2.5y + y2 = -1.25

The y term is -2.5y.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5y + 1.5625 + y2 = -1.25 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = -1.25 + 1.5625

Combine like terms: -1.25 + 1.5625 = 0.3125
1.5625 + -2.5y + y2 = 0.3125

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(y + -1.25) equal to 0.559016994 and -0.559016994.

Subproblem 1
y + -1.25 = 0.559016994

Simplifying
y + -1.25 = 0.559016994

Reorder the terms:
-1.25 + y = 0.559016994

Solving
-1.25 + y = 0.559016994

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = 0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 0.559016994 + 1.25
y = 0.559016994 + 1.25

Combine like terms: 0.559016994 + 1.25 = 1.809016994
y = 1.809016994

Simplifying
y = 1.809016994

Subproblem 2
y + -1.25 = -0.559016994

Simplifying
y + -1.25 = -0.559016994

Reorder the terms:
-1.25 + y = -0.559016994

Solving
-1.25 + y = -0.559016994

Solving for variable 'y'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + y = -0.559016994 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -0.559016994 + 1.25
y = -0.559016994 + 1.25

Combine like terms: -0.559016994 + 1.25 = 0.690983006
y = 0.690983006

Simplifying
y = 0.690983006

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.809016994, 0.690983006}