5(y+2)[-4(y-1)]=6

Solution for 5(y+2)[-4(y-1)]=6 equation:

Simplifying
5(y + 2)[-4(y + -1)] = 6

Reorder the terms:
5(2 + y)[-4(y + -1)] = 6

Reorder the terms:
5(2 + y)[-4(-1 + y)] = 6
5(2 + y)[(-1 * -4 + y * -4)] = 6
5(2 + y)[(4 + -4y)] = 6

Multiply (2 + y) * [4 + -4y]
5(2[4 + -4y] + y[4 + -4y]) = 6
5([4 * 2 + -4y * 2] + y[4 + -4y]) = 6
5([8 + -8y] + y[4 + -4y]) = 6
5(8 + -8y + [4 * y + -4y * y]) = 6
5(8 + -8y + [4y + -4y2]) = 6

Combine like terms: -8y + 4y = -4y
5(8 + -4y + -4y2) = 6
(8 * 5 + -4y * 5 + -4y2 * 5) = 6
(40 + -20y + -20y2) = 6

Solving
40 + -20y + -20y2 = 6

Solving for variable 'y'.

Reorder the terms:
40 + -6 + -20y + -20y2 = 6 + -6

Combine like terms: 40 + -6 = 34
34 + -20y + -20y2 = 6 + -6

Combine like terms: 6 + -6 = 0
34 + -20y + -20y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + -10y + -10y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + -10y + -10y2)' equal to zero and attempt to solve:

Simplifying
17 + -10y + -10y2 = 0

Solving
17 + -10y + -10y2 = 0

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

Divide each side by '-10'.
-1.7 + y + y2 = 0.0

Move the constant term to the right:

Add '1.7' to each side of the equation.
-1.7 + y + 1.7 + y2 = 0.0 + 1.7

Reorder the terms:
-1.7 + 1.7 + y + y2 = 0.0 + 1.7

Combine like terms: -1.7 + 1.7 = 0.0
0.0 + y + y2 = 0.0 + 1.7
y + y2 = 0.0 + 1.7

Combine like terms: 0.0 + 1.7 = 1.7
y + y2 = 1.7

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 1.7 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 1.7 + 0.25

Combine like terms: 1.7 + 0.25 = 1.95
1.25 + y2 = 1.95

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 1.95

Calculate the square root of the right side: 1.396424004

Break this problem into two subproblems by setting 
(y + 0.5) equal to 1.396424004 and -1.396424004.

Subproblem 1
y + 0.5 = 1.396424004

Simplifying
y + 0.5 = 1.396424004

Reorder the terms:
0.5 + y = 1.396424004

Solving
0.5 + y = 1.396424004

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 1.396424004 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 1.396424004 + -0.5
y = 1.396424004 + -0.5

Combine like terms: 1.396424004 + -0.5 = 0.896424004
y = 0.896424004

Simplifying
y = 0.896424004

Subproblem 2
y + 0.5 = -1.396424004

Simplifying
y + 0.5 = -1.396424004

Reorder the terms:
0.5 + y = -1.396424004

Solving
0.5 + y = -1.396424004

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -1.396424004 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -1.396424004 + -0.5
y = -1.396424004 + -0.5

Combine like terms: -1.396424004 + -0.5 = -1.896424004
y = -1.896424004

Simplifying
y = -1.896424004

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.896424004, -1.896424004}
Solution
y = {0.896424004, -1.896424004}