y(y-5)(10)+(y+5)(y-5)(2)=7y-5(y)

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Solution for y(y-5)(10)+(y+5)(y-5)(2)=7y-5(y) equation: 


Simplifying
y(y + -5)(10) + (y + 5)(y + -5)(2) = 7y + -5(y)

Reorder the terms:
y(-5 + y)(10) + (y + 5)(y + -5)(2) = 7y + -5(y)

Reorder the terms for easier multiplication:
10y(-5 + y) + (y + 5)(y + -5)(2) = 7y + -5(y)
(-5 * 10y + y * 10y) + (y + 5)(y + -5)(2) = 7y + -5(y)
(-50y + 10y2) + (y + 5)(y + -5)(2) = 7y + -5(y)

Reorder the terms:
-50y + 10y2 + (5 + y)(y + -5)(2) = 7y + -5(y)

Reorder the terms:
-50y + 10y2 + (5 + y)(-5 + y)(2) = 7y + -5(y)

Reorder the terms for easier multiplication:
-50y + 10y2 + 2(5 + y)(-5 + y) = 7y + -5(y)

Multiply (5 + y) * (-5 + y)
-50y + 10y2 + 2(5(-5 + y) + y(-5 + y)) = 7y + -5(y)
-50y + 10y2 + 2((-5 * 5 + y * 5) + y(-5 + y)) = 7y + -5(y)
-50y + 10y2 + 2((-25 + 5y) + y(-5 + y)) = 7y + -5(y)
-50y + 10y2 + 2(-25 + 5y + (-5 * y + y * y)) = 7y + -5(y)
-50y + 10y2 + 2(-25 + 5y + (-5y + y2)) = 7y + -5(y)

Combine like terms: 5y + -5y = 0
-50y + 10y2 + 2(-25 + 0 + y2) = 7y + -5(y)
-50y + 10y2 + 2(-25 + y2) = 7y + -5(y)
-50y + 10y2 + (-25 * 2 + y2 * 2) = 7y + -5(y)
-50y + 10y2 + (-50 + 2y2) = 7y + -5(y)

Reorder the terms:
-50 + -50y + 10y2 + 2y2 = 7y + -5(y)

Combine like terms: 10y2 + 2y2 = 12y2
-50 + -50y + 12y2 = 7y + -5(y)

Combine like terms: 7y + -5y = 2y
-50 + -50y + 12y2 = 2y

Solving
-50 + -50y + 12y2 = 2y

Solving for variable 'y'.

Reorder the terms:
-50 + -50y + -2y + 12y2 = 2y + -2y

Combine like terms: -50y + -2y = -52y
-50 + -52y + 12y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-50 + -52y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -26y + 6y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + -26y + 6y2)' equal to zero and attempt to solve:

Simplifying
-25 + -26y + 6y2 = 0

Solving
-25 + -26y + 6y2 = 0

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

Divide each side by '6'.
-4.166666667 + -4.333333333y + y2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + -4.333333333y + 4.166666667 + y2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + -4.333333333y + y2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + -4.333333333y + y2 = 0 + 4.166666667
-4.333333333y + y2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
-4.333333333y + y2 = 4.166666667

The y term is -4.333333333y.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333y + 4.694444446 + y2 = 4.166666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333y + y2 = 4.166666667 + 4.694444446

Combine like terms: 4.166666667 + 4.694444446 = 8.861111113
4.694444446 + -4.333333333y + y2 = 8.861111113

Factor a perfect square on the left side:
(y + -2.166666667)(y + -2.166666667) = 8.861111113

Calculate the square root of the right side: 2.97676185

Break this problem into two subproblems by setting 
(y + -2.166666667) equal to 2.97676185 and -2.97676185.


Subproblem 1
y + -2.166666667 = 2.97676185

Simplifying
y + -2.166666667 = 2.97676185

Reorder the terms:
-2.166666667 + y = 2.97676185

Solving
-2.166666667 + y = 2.97676185

Solving for variable 'y'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + y = 2.97676185 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + y = 2.97676185 + 2.166666667
y = 2.97676185 + 2.166666667

Combine like terms: 2.97676185 + 2.166666667 = 5.143428517
y = 5.143428517

Simplifying
y = 5.143428517


Subproblem 2
y + -2.166666667 = -2.97676185

Simplifying
y + -2.166666667 = -2.97676185

Reorder the terms:
-2.166666667 + y = -2.97676185

Solving
-2.166666667 + y = -2.97676185

Solving for variable 'y'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + y = -2.97676185 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + y = -2.97676185 + 2.166666667
y = -2.97676185 + 2.166666667

Combine like terms: -2.97676185 + 2.166666667 = -0.810095183
y = -0.810095183

Simplifying
y = -0.810095183


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.143428517, -0.810095183}
Solution
y = {5.143428517, -0.810095183}

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