y=5y-2(7y^2+4y-8)+9y^2

Solution for y=5y-2(7y^2+4y-8)+9y^2 equation:

Simplifying
y = 5y + -2(7y2 + 4y + -8) + 9y2

Reorder the terms:
y = 5y + -2(-8 + 4y + 7y2) + 9y2
y = 5y + (-8 * -2 + 4y * -2 + 7y2 * -2) + 9y2
y = 5y + (16 + -8y + -14y2) + 9y2

Reorder the terms:
y = 16 + 5y + -8y + -14y2 + 9y2

Combine like terms: 5y + -8y = -3y
y = 16 + -3y + -14y2 + 9y2

Combine like terms: -14y2 + 9y2 = -5y2
y = 16 + -3y + -5y2

Solving
y = 16 + -3y + -5y2

Solving for variable 'y'.

Reorder the terms:
-16 + y + 3y + 5y2 = 16 + -3y + -5y2 + -16 + 3y + 5y2

Combine like terms: y + 3y = 4y
-16 + 4y + 5y2 = 16 + -3y + -5y2 + -16 + 3y + 5y2

Reorder the terms:
-16 + 4y + 5y2 = 16 + -16 + -3y + 3y + -5y2 + 5y2

Combine like terms: 16 + -16 = 0
-16 + 4y + 5y2 = 0 + -3y + 3y + -5y2 + 5y2
-16 + 4y + 5y2 = -3y + 3y + -5y2 + 5y2

Combine like terms: -3y + 3y = 0
-16 + 4y + 5y2 = 0 + -5y2 + 5y2
-16 + 4y + 5y2 = -5y2 + 5y2

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

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

Divide each side by '5'.
-3.2 + 0.8y + y2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 0.8y + 3.2 + y2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 0.8y + y2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 0.8y + y2 = 0 + 3.2
0.8y + y2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
0.8y + y2 = 3.2

The y term is 0.8y.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8y + 0.16 + y2 = 3.2 + 0.16

Reorder the terms:
0.16 + 0.8y + y2 = 3.2 + 0.16

Combine like terms: 3.2 + 0.16 = 3.36
0.16 + 0.8y + y2 = 3.36

Factor a perfect square on the left side:
(y + 0.4)(y + 0.4) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(y + 0.4) equal to 1.833030278 and -1.833030278.

Subproblem 1
y + 0.4 = 1.833030278

Simplifying
y + 0.4 = 1.833030278

Reorder the terms:
0.4 + y = 1.833030278

Solving
0.4 + y = 1.833030278

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = 1.833030278 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = 1.833030278 + -0.4
y = 1.833030278 + -0.4

Combine like terms: 1.833030278 + -0.4 = 1.433030278
y = 1.433030278

Simplifying
y = 1.433030278

Subproblem 2
y + 0.4 = -1.833030278

Simplifying
y + 0.4 = -1.833030278

Reorder the terms:
0.4 + y = -1.833030278

Solving
0.4 + y = -1.833030278

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = -1.833030278 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = -1.833030278 + -0.4
y = -1.833030278 + -0.4

Combine like terms: -1.833030278 + -0.4 = -2.233030278
y = -2.233030278

Simplifying
y = -2.233030278

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.433030278, -2.233030278}