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

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

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

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

Remove parenthesis around (-4 + -5y + 3y2)
-4 + -5y + 3y2 + (y2 + -7y + 6) = 0

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

Remove parenthesis around (6 + -7y + y2)
-4 + -5y + 3y2 + 6 + -7y + y2 = 0

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

Combine like terms: -4 + 6 = 2
2 + -5y + -7y + 3y2 + y2 = 0

Combine like terms: -5y + -7y = -12y
2 + -12y + 3y2 + y2 = 0

Combine like terms: 3y2 + y2 = 4y2
2 + -12y + 4y2 = 0

Solving
2 + -12y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -6y + 2y2) = 0

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

Simplifying
1 + -6y + 2y2 = 0

Solving
1 + -6y + 2y2 = 0

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

Divide each side by '2'.
0.5 + -3y + y2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -3y + -0.5 + y2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -3y + y2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -3y + y2 = 0 + -0.5
-3y + y2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-3y + y2 = -0.5

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -0.5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + -3y + y2 = 1.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(y + -1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
y + -1.5 = 1.322875656

Simplifying
y + -1.5 = 1.322875656

Reorder the terms:
-1.5 + y = 1.322875656

Solving
-1.5 + y = 1.322875656

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 1.322875656 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 1.322875656 + 1.5
y = 1.322875656 + 1.5

Combine like terms: 1.322875656 + 1.5 = 2.822875656
y = 2.822875656

Simplifying
y = 2.822875656

Subproblem 2
y + -1.5 = -1.322875656

Simplifying
y + -1.5 = -1.322875656

Reorder the terms:
-1.5 + y = -1.322875656

Solving
-1.5 + y = -1.322875656

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -1.322875656 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -1.322875656 + 1.5
y = -1.322875656 + 1.5

Combine like terms: -1.322875656 + 1.5 = 0.177124344
y = 0.177124344

Simplifying
y = 0.177124344

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.822875656, 0.177124344}
Solution
y = {2.822875656, 0.177124344}