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

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

Simplifying
7y + -3(4y2 + -6) + -1(-5y2 + y + -2) = 0

Reorder the terms:
7y + -3(-6 + 4y2) + -1(-5y2 + y + -2) = 0
7y + (-6 * -3 + 4y2 * -3) + -1(-5y2 + y + -2) = 0
7y + (18 + -12y2) + -1(-5y2 + y + -2) = 0

Reorder the terms:
7y + 18 + -12y2 + -1(-2 + y + -5y2) = 0
7y + 18 + -12y2 + (-2 * -1 + y * -1 + -5y2 * -1) = 0
7y + 18 + -12y2 + (2 + -1y + 5y2) = 0

Reorder the terms:
18 + 2 + 7y + -1y + -12y2 + 5y2 = 0

Combine like terms: 18 + 2 = 20
20 + 7y + -1y + -12y2 + 5y2 = 0

Combine like terms: 7y + -1y = 6y
20 + 6y + -12y2 + 5y2 = 0

Combine like terms: -12y2 + 5y2 = -7y2
20 + 6y + -7y2 = 0

Solving
20 + 6y + -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'.
-2.857142857 + -0.8571428571y + y2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + -0.8571428571y + 2.857142857 + y2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + -0.8571428571y + y2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + -0.8571428571y + y2 = 0 + 2.857142857
-0.8571428571y + y2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
-0.8571428571y + y2 = 2.857142857

The y term is -0.8571428571y.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571y + 0.1836734694 + y2 = 2.857142857 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571y + y2 = 2.857142857 + 0.1836734694

Combine like terms: 2.857142857 + 0.1836734694 = 3.0408163264
0.1836734694 + -0.8571428571y + y2 = 3.0408163264

Factor a perfect square on the left side:
(y + -0.4285714286)(y + -0.4285714286) = 3.0408163264

Calculate the square root of the right side: 1.743793659

Break this problem into two subproblems by setting 
(y + -0.4285714286) equal to 1.743793659 and -1.743793659.

Subproblem 1
y + -0.4285714286 = 1.743793659

Simplifying
y + -0.4285714286 = 1.743793659

Reorder the terms:
-0.4285714286 + y = 1.743793659

Solving
-0.4285714286 + y = 1.743793659

Solving for variable 'y'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + y = 1.743793659 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + y = 1.743793659 + 0.4285714286
y = 1.743793659 + 0.4285714286

Combine like terms: 1.743793659 + 0.4285714286 = 2.1723650876
y = 2.1723650876

Simplifying
y = 2.1723650876

Subproblem 2
y + -0.4285714286 = -1.743793659

Simplifying
y + -0.4285714286 = -1.743793659

Reorder the terms:
-0.4285714286 + y = -1.743793659

Solving
-0.4285714286 + y = -1.743793659

Solving for variable 'y'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + y = -1.743793659 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + y = -1.743793659 + 0.4285714286
y = -1.743793659 + 0.4285714286

Combine like terms: -1.743793659 + 0.4285714286 = -1.3152222304
y = -1.3152222304

Simplifying
y = -1.3152222304

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.1723650876, -1.3152222304}