9y^2-4y-8-2y^2+20y+3=

Solution for 9y^2-4y-8-2y^2+20y+3= equation:

Simplifying
9y2 + -4y + -8 + -2y2 + 20y + 3 = 0

Reorder the terms:
-8 + 3 + -4y + 20y + 9y2 + -2y2 = 0

Combine like terms: -8 + 3 = -5
-5 + -4y + 20y + 9y2 + -2y2 = 0

Combine like terms: -4y + 20y = 16y
-5 + 16y + 9y2 + -2y2 = 0

Combine like terms: 9y2 + -2y2 = 7y2
-5 + 16y + 7y2 = 0

Solving
-5 + 16y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
-0.7142857143 + 2.285714286y + y2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 2.285714286y + 0.7142857143 + y2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 2.285714286y + y2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 2.285714286y + y2 = 0 + 0.7142857143
2.285714286y + y2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
2.285714286y + y2 = 0.7142857143

The y term is 2.285714286y.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286y + 1.306122449 + y2 = 0.7142857143 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286y + y2 = 0.7142857143 + 1.306122449

Combine like terms: 0.7142857143 + 1.306122449 = 2.0204081633
1.306122449 + 2.285714286y + y2 = 2.0204081633

Factor a perfect square on the left side:
(y + 1.142857143)(y + 1.142857143) = 2.0204081633

Calculate the square root of the right side: 1.421410624

Break this problem into two subproblems by setting 
(y + 1.142857143) equal to 1.421410624 and -1.421410624.

Subproblem 1
y + 1.142857143 = 1.421410624

Simplifying
y + 1.142857143 = 1.421410624

Reorder the terms:
1.142857143 + y = 1.421410624

Solving
1.142857143 + y = 1.421410624

Solving for variable 'y'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + y = 1.421410624 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + y = 1.421410624 + -1.142857143
y = 1.421410624 + -1.142857143

Combine like terms: 1.421410624 + -1.142857143 = 0.278553481
y = 0.278553481

Simplifying
y = 0.278553481

Subproblem 2
y + 1.142857143 = -1.421410624

Simplifying
y + 1.142857143 = -1.421410624

Reorder the terms:
1.142857143 + y = -1.421410624

Solving
1.142857143 + y = -1.421410624

Solving for variable 'y'.

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

Add '-1.142857143' to each side of the equation.
1.142857143 + -1.142857143 + y = -1.421410624 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + y = -1.421410624 + -1.142857143
y = -1.421410624 + -1.142857143

Combine like terms: -1.421410624 + -1.142857143 = -2.564267767
y = -2.564267767

Simplifying
y = -2.564267767

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.278553481, -2.564267767}