8y(5y+5)-5y^2=5(5y+5)

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Solution for 8y(5y+5)-5y^2=5(5y+5) equation: 


Simplifying
8y(5y + 5) + -5y2 = 5(5y + 5)

Reorder the terms:
8y(5 + 5y) + -5y2 = 5(5y + 5)
(5 * 8y + 5y * 8y) + -5y2 = 5(5y + 5)
(40y + 40y2) + -5y2 = 5(5y + 5)

Combine like terms: 40y2 + -5y2 = 35y2
40y + 35y2 = 5(5y + 5)

Reorder the terms:
40y + 35y2 = 5(5 + 5y)
40y + 35y2 = (5 * 5 + 5y * 5)
40y + 35y2 = (25 + 25y)

Solving
40y + 35y2 = 25 + 25y

Solving for variable 'y'.

Reorder the terms:
-25 + 40y + -25y + 35y2 = 25 + 25y + -25 + -25y

Combine like terms: 40y + -25y = 15y
-25 + 15y + 35y2 = 25 + 25y + -25 + -25y

Reorder the terms:
-25 + 15y + 35y2 = 25 + -25 + 25y + -25y

Combine like terms: 25 + -25 = 0
-25 + 15y + 35y2 = 0 + 25y + -25y
-25 + 15y + 35y2 = 25y + -25y

Combine like terms: 25y + -25y = 0
-25 + 15y + 35y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 3y + 7y2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + 3y + 7y2)' equal to zero and attempt to solve:

Simplifying
-5 + 3y + 7y2 = 0

Solving
-5 + 3y + 7y2 = 0

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

Divide each side by '7'.
-0.7142857143 + 0.4285714286y + y2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 0.4285714286y + 0.7142857143 + y2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 0.4285714286y + y2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 0.4285714286y + y2 = 0 + 0.7142857143
0.4285714286y + y2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
0.4285714286y + y2 = 0.7142857143

The y term is 0.4285714286y.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286y + 0.04591836735 + y2 = 0.7142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286y + y2 = 0.7142857143 + 0.04591836735

Combine like terms: 0.7142857143 + 0.04591836735 = 0.76020408165
0.04591836735 + 0.4285714286y + y2 = 0.76020408165

Factor a perfect square on the left side:
(y + 0.2142857143)(y + 0.2142857143) = 0.76020408165

Calculate the square root of the right side: 0.87189683

Break this problem into two subproblems by setting 
(y + 0.2142857143) equal to 0.87189683 and -0.87189683.


Subproblem 1
y + 0.2142857143 = 0.87189683

Simplifying
y + 0.2142857143 = 0.87189683

Reorder the terms:
0.2142857143 + y = 0.87189683

Solving
0.2142857143 + y = 0.87189683

Solving for variable 'y'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + y = 0.87189683 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + y = 0.87189683 + -0.2142857143
y = 0.87189683 + -0.2142857143

Combine like terms: 0.87189683 + -0.2142857143 = 0.6576111157
y = 0.6576111157

Simplifying
y = 0.6576111157


Subproblem 2
y + 0.2142857143 = -0.87189683

Simplifying
y + 0.2142857143 = -0.87189683

Reorder the terms:
0.2142857143 + y = -0.87189683

Solving
0.2142857143 + y = -0.87189683

Solving for variable 'y'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + y = -0.87189683 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + y = -0.87189683 + -0.2142857143
y = -0.87189683 + -0.2142857143

Combine like terms: -0.87189683 + -0.2142857143 = -1.0861825443
y = -1.0861825443

Simplifying
y = -1.0861825443


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.6576111157, -1.0861825443}
Solution
y = {0.6576111157, -1.0861825443}

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