-2(y+1)5y=3(y+1)-2

Solution for -2(y+1)5y=3(y+1)-2 equation:

Simplifying
-2(y + 1) * 5y = 3(y + 1) + -2

Reorder the terms:
-2(1 + y) * 5y = 3(y + 1) + -2

Reorder the terms for easier multiplication:
-2 * 5y(1 + y) = 3(y + 1) + -2

Multiply -2 * 5
-10y(1 + y) = 3(y + 1) + -2
(1 * -10y + y * -10y) = 3(y + 1) + -2
(-10y + -10y2) = 3(y + 1) + -2

Reorder the terms:
-10y + -10y2 = 3(1 + y) + -2
-10y + -10y2 = (1 * 3 + y * 3) + -2
-10y + -10y2 = (3 + 3y) + -2

Reorder the terms:
-10y + -10y2 = 3 + -2 + 3y

Combine like terms: 3 + -2 = 1
-10y + -10y2 = 1 + 3y

Solving
-10y + -10y2 = 1 + 3y

Solving for variable 'y'.

Reorder the terms:
-1 + -10y + -3y + -10y2 = 1 + 3y + -1 + -3y

Combine like terms: -10y + -3y = -13y
-1 + -13y + -10y2 = 1 + 3y + -1 + -3y

Reorder the terms:
-1 + -13y + -10y2 = 1 + -1 + 3y + -3y

Combine like terms: 1 + -1 = 0
-1 + -13y + -10y2 = 0 + 3y + -3y
-1 + -13y + -10y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-1 + -13y + -10y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 13y + 10y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 13y + 10y2)' equal to zero and attempt to solve:

Simplifying
1 + 13y + 10y2 = 0

Solving
1 + 13y + 10y2 = 0

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

Divide each side by '10'.
0.1 + 1.3y + y2 = 0.0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + 1.3y + -0.1 + y2 = 0.0 + -0.1

Reorder the terms:
0.1 + -0.1 + 1.3y + y2 = 0.0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + 1.3y + y2 = 0.0 + -0.1
1.3y + y2 = 0.0 + -0.1

Combine like terms: 0.0 + -0.1 = -0.1
1.3y + y2 = -0.1

The y term is 1.3y.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3y + 0.4225 + y2 = -0.1 + 0.4225

Reorder the terms:
0.4225 + 1.3y + y2 = -0.1 + 0.4225

Combine like terms: -0.1 + 0.4225 = 0.3225
0.4225 + 1.3y + y2 = 0.3225

Factor a perfect square on the left side:
(y + 0.65)(y + 0.65) = 0.3225

Calculate the square root of the right side: 0.567890835

Break this problem into two subproblems by setting 
(y + 0.65) equal to 0.567890835 and -0.567890835.

Subproblem 1
y + 0.65 = 0.567890835

Simplifying
y + 0.65 = 0.567890835

Reorder the terms:
0.65 + y = 0.567890835

Solving
0.65 + y = 0.567890835

Solving for variable 'y'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + y = 0.567890835 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + y = 0.567890835 + -0.65
y = 0.567890835 + -0.65

Combine like terms: 0.567890835 + -0.65 = -0.082109165
y = -0.082109165

Simplifying
y = -0.082109165

Subproblem 2
y + 0.65 = -0.567890835

Simplifying
y + 0.65 = -0.567890835

Reorder the terms:
0.65 + y = -0.567890835

Solving
0.65 + y = -0.567890835

Solving for variable 'y'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + y = -0.567890835 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + y = -0.567890835 + -0.65
y = -0.567890835 + -0.65

Combine like terms: -0.567890835 + -0.65 = -1.217890835
y = -1.217890835

Simplifying
y = -1.217890835

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.082109165, -1.217890835}
Solution
y = {-0.082109165, -1.217890835}