-5y^2-y=-3

Solution for -5y^2-y=-3 equation:

Simplifying
-5y2 + -1y = -3

Reorder the terms:
-1y + -5y2 = -3

Solving
-1y + -5y2 = -3

Solving for variable 'y'.

Reorder the terms:
3 + -1y + -5y2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + -1y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.6 + 0.2y + y2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.2y + 0.6 + y2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.2y + y2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.2y + y2 = 0 + 0.6
0.2y + y2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.2y + y2 = 0.6

The y term is 0.2y.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2y + 0.01 + y2 = 0.6 + 0.01

Reorder the terms:
0.01 + 0.2y + y2 = 0.6 + 0.01

Combine like terms: 0.6 + 0.01 = 0.61
0.01 + 0.2y + y2 = 0.61

Factor a perfect square on the left side:
(y + 0.1)(y + 0.1) = 0.61

Calculate the square root of the right side: 0.781024968

Break this problem into two subproblems by setting 
(y + 0.1) equal to 0.781024968 and -0.781024968.

Subproblem 1
y + 0.1 = 0.781024968

Simplifying
y + 0.1 = 0.781024968

Reorder the terms:
0.1 + y = 0.781024968

Solving
0.1 + y = 0.781024968

Solving for variable 'y'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + y = 0.781024968 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + y = 0.781024968 + -0.1
y = 0.781024968 + -0.1

Combine like terms: 0.781024968 + -0.1 = 0.681024968
y = 0.681024968

Simplifying
y = 0.681024968

Subproblem 2
y + 0.1 = -0.781024968

Simplifying
y + 0.1 = -0.781024968

Reorder the terms:
0.1 + y = -0.781024968

Solving
0.1 + y = -0.781024968

Solving for variable 'y'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + y = -0.781024968 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + y = -0.781024968 + -0.1
y = -0.781024968 + -0.1

Combine like terms: -0.781024968 + -0.1 = -0.881024968
y = -0.881024968

Simplifying
y = -0.881024968

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.681024968, -0.881024968}