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

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

Simplifying
(6y + y + 5) + (-4y2 + 3y + 7) = 0

Reorder the terms:
(5 + 6y + y) + (-4y2 + 3y + 7) = 0

Combine like terms: 6y + y = 7y
(5 + 7y) + (-4y2 + 3y + 7) = 0

Remove parenthesis around (5 + 7y)
5 + 7y + (-4y2 + 3y + 7) = 0

Reorder the terms:
5 + 7y + (7 + 3y + -4y2) = 0

Remove parenthesis around (7 + 3y + -4y2)
5 + 7y + 7 + 3y + -4y2 = 0

Reorder the terms:
5 + 7 + 7y + 3y + -4y2 = 0

Combine like terms: 5 + 7 = 12
12 + 7y + 3y + -4y2 = 0

Combine like terms: 7y + 3y = 10y
12 + 10y + -4y2 = 0

Solving
12 + 10y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5y + -2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 5y + -2y2)' equal to zero and attempt to solve:

Simplifying
6 + 5y + -2y2 = 0

Solving
6 + 5y + -2y2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3 + -2.5y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -2.5y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -2.5y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2.5y + y2 = 0 + 3
-2.5y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-2.5y + y2 = 3

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 = 3 + 1.5625

Reorder the terms:
1.5625 + -2.5y + y2 = 3 + 1.5625

Combine like terms: 3 + 1.5625 = 4.5625
1.5625 + -2.5y + y2 = 4.5625

Factor a perfect square on the left side:
(y + -1.25)(y + -1.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(y + -1.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
y + -1.25 = 2.136000936

Simplifying
y + -1.25 = 2.136000936

Reorder the terms:
-1.25 + y = 2.136000936

Solving
-1.25 + y = 2.136000936

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 = 2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = 2.136000936 + 1.25
y = 2.136000936 + 1.25

Combine like terms: 2.136000936 + 1.25 = 3.386000936
y = 3.386000936

Simplifying
y = 3.386000936

Subproblem 2
y + -1.25 = -2.136000936

Simplifying
y + -1.25 = -2.136000936

Reorder the terms:
-1.25 + y = -2.136000936

Solving
-1.25 + y = -2.136000936

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 = -2.136000936 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + y = -2.136000936 + 1.25
y = -2.136000936 + 1.25

Combine like terms: -2.136000936 + 1.25 = -0.886000936
y = -0.886000936

Simplifying
y = -0.886000936

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.386000936, -0.886000936}
Solution
y = {3.386000936, -0.886000936}