(6y*y-2y+3)=(-5y*y+7y+4)

Solution for (6y*y-2y+3)=(-5y*y+7y+4) equation:

Simplifying
(6y * y + -2y + 3) = (-5y * y + 7y + 4)

Multiply y * y
(6y2 + -2y + 3) = (-5y * y + 7y + 4)

Reorder the terms:
(3 + -2y + 6y2) = (-5y * y + 7y + 4)

Remove parenthesis around (3 + -2y + 6y2)
3 + -2y + 6y2 = (-5y * y + 7y + 4)

Multiply y * y
3 + -2y + 6y2 = (-5y2 + 7y + 4)

Reorder the terms:
3 + -2y + 6y2 = (4 + 7y + -5y2)

Remove parenthesis around (4 + 7y + -5y2)
3 + -2y + 6y2 = 4 + 7y + -5y2

Solving
3 + -2y + 6y2 = 4 + 7y + -5y2

Solving for variable 'y'.

Reorder the terms:
3 + -4 + -2y + -7y + 6y2 + 5y2 = 4 + 7y + -5y2 + -4 + -7y + 5y2

Combine like terms: 3 + -4 = -1
-1 + -2y + -7y + 6y2 + 5y2 = 4 + 7y + -5y2 + -4 + -7y + 5y2

Combine like terms: -2y + -7y = -9y
-1 + -9y + 6y2 + 5y2 = 4 + 7y + -5y2 + -4 + -7y + 5y2

Combine like terms: 6y2 + 5y2 = 11y2
-1 + -9y + 11y2 = 4 + 7y + -5y2 + -4 + -7y + 5y2

Reorder the terms:
-1 + -9y + 11y2 = 4 + -4 + 7y + -7y + -5y2 + 5y2

Combine like terms: 4 + -4 = 0
-1 + -9y + 11y2 = 0 + 7y + -7y + -5y2 + 5y2
-1 + -9y + 11y2 = 7y + -7y + -5y2 + 5y2

Combine like terms: 7y + -7y = 0
-1 + -9y + 11y2 = 0 + -5y2 + 5y2
-1 + -9y + 11y2 = -5y2 + 5y2

Combine like terms: -5y2 + 5y2 = 0
-1 + -9y + 11y2 = 0

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

Divide each side by '11'.
-0.09090909091 + -0.8181818182y + y2 = 0

Move the constant term to the right:

Add '0.09090909091' to each side of the equation.
-0.09090909091 + -0.8181818182y + 0.09090909091 + y2 = 0 + 0.09090909091

Reorder the terms:
-0.09090909091 + 0.09090909091 + -0.8181818182y + y2 = 0 + 0.09090909091

Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000
0.00000000000 + -0.8181818182y + y2 = 0 + 0.09090909091
-0.8181818182y + y2 = 0 + 0.09090909091

Combine like terms: 0 + 0.09090909091 = 0.09090909091
-0.8181818182y + y2 = 0.09090909091

The y term is -0.8181818182y.  Take half its coefficient (-0.4090909091).
Square it (0.1673553719) and add it to both sides.

Add '0.1673553719' to each side of the equation.
-0.8181818182y + 0.1673553719 + y2 = 0.09090909091 + 0.1673553719

Reorder the terms:
0.1673553719 + -0.8181818182y + y2 = 0.09090909091 + 0.1673553719

Combine like terms: 0.09090909091 + 0.1673553719 = 0.25826446281
0.1673553719 + -0.8181818182y + y2 = 0.25826446281

Factor a perfect square on the left side:
(y + -0.4090909091)(y + -0.4090909091) = 0.25826446281

Calculate the square root of the right side: 0.508197268

Break this problem into two subproblems by setting 
(y + -0.4090909091) equal to 0.508197268 and -0.508197268.

Subproblem 1
y + -0.4090909091 = 0.508197268

Simplifying
y + -0.4090909091 = 0.508197268

Reorder the terms:
-0.4090909091 + y = 0.508197268

Solving
-0.4090909091 + y = 0.508197268

Solving for variable 'y'.

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

Add '0.4090909091' to each side of the equation.
-0.4090909091 + 0.4090909091 + y = 0.508197268 + 0.4090909091

Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000
0.0000000000 + y = 0.508197268 + 0.4090909091
y = 0.508197268 + 0.4090909091

Combine like terms: 0.508197268 + 0.4090909091 = 0.9172881771
y = 0.9172881771

Simplifying
y = 0.9172881771

Subproblem 2
y + -0.4090909091 = -0.508197268

Simplifying
y + -0.4090909091 = -0.508197268

Reorder the terms:
-0.4090909091 + y = -0.508197268

Solving
-0.4090909091 + y = -0.508197268

Solving for variable 'y'.

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

Add '0.4090909091' to each side of the equation.
-0.4090909091 + 0.4090909091 + y = -0.508197268 + 0.4090909091

Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000
0.0000000000 + y = -0.508197268 + 0.4090909091
y = -0.508197268 + 0.4090909091

Combine like terms: -0.508197268 + 0.4090909091 = -0.0991063589
y = -0.0991063589

Simplifying
y = -0.0991063589

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.9172881771, -0.0991063589}