6(y+7)-10y(y+2)=-10

Solution for 6(y+7)-10y(y+2)=-10 equation:

Simplifying
6(y + 7) + -10y(y + 2) = -10

Reorder the terms:
6(7 + y) + -10y(y + 2) = -10
(7 * 6 + y * 6) + -10y(y + 2) = -10
(42 + 6y) + -10y(y + 2) = -10

Reorder the terms:
42 + 6y + -10y(2 + y) = -10
42 + 6y + (2 * -10y + y * -10y) = -10
42 + 6y + (-20y + -10y2) = -10

Combine like terms: 6y + -20y = -14y
42 + -14y + -10y2 = -10

Solving
42 + -14y + -10y2 = -10

Solving for variable 'y'.

Reorder the terms:
42 + 10 + -14y + -10y2 = -10 + 10

Combine like terms: 42 + 10 = 52
52 + -14y + -10y2 = -10 + 10

Combine like terms: -10 + 10 = 0
52 + -14y + -10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(26 + -7y + -5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(26 + -7y + -5y2)' equal to zero and attempt to solve:

Simplifying
26 + -7y + -5y2 = 0

Solving
26 + -7y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-5.2 + 1.4y + y2 = 0

Move the constant term to the right:

Add '5.2' to each side of the equation.
-5.2 + 1.4y + 5.2 + y2 = 0 + 5.2

Reorder the terms:
-5.2 + 5.2 + 1.4y + y2 = 0 + 5.2

Combine like terms: -5.2 + 5.2 = 0.0
0.0 + 1.4y + y2 = 0 + 5.2
1.4y + y2 = 0 + 5.2

Combine like terms: 0 + 5.2 = 5.2
1.4y + y2 = 5.2

The y term is 1.4y.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4y + 0.49 + y2 = 5.2 + 0.49

Reorder the terms:
0.49 + 1.4y + y2 = 5.2 + 0.49

Combine like terms: 5.2 + 0.49 = 5.69
0.49 + 1.4y + y2 = 5.69

Factor a perfect square on the left side:
(y + 0.7)(y + 0.7) = 5.69

Calculate the square root of the right side: 2.385372088

Break this problem into two subproblems by setting 
(y + 0.7) equal to 2.385372088 and -2.385372088.

Subproblem 1
y + 0.7 = 2.385372088

Simplifying
y + 0.7 = 2.385372088

Reorder the terms:
0.7 + y = 2.385372088

Solving
0.7 + y = 2.385372088

Solving for variable 'y'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + y = 2.385372088 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + y = 2.385372088 + -0.7
y = 2.385372088 + -0.7

Combine like terms: 2.385372088 + -0.7 = 1.685372088
y = 1.685372088

Simplifying
y = 1.685372088

Subproblem 2
y + 0.7 = -2.385372088

Simplifying
y + 0.7 = -2.385372088

Reorder the terms:
0.7 + y = -2.385372088

Solving
0.7 + y = -2.385372088

Solving for variable 'y'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + y = -2.385372088 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + y = -2.385372088 + -0.7
y = -2.385372088 + -0.7

Combine like terms: -2.385372088 + -0.7 = -3.085372088
y = -3.085372088

Simplifying
y = -3.085372088

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.685372088, -3.085372088}
Solution
y = {1.685372088, -3.085372088}