4y=2y(y-5)-2

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Solution for 4y=2y(y-5)-2 equation: 


Simplifying
4y = 2y(y + -5) + -2

Reorder the terms:
4y = 2y(-5 + y) + -2
4y = (-5 * 2y + y * 2y) + -2
4y = (-10y + 2y2) + -2

Reorder the terms:
4y = -2 + -10y + 2y2

Solving
4y = -2 + -10y + 2y2

Solving for variable 'y'.

Reorder the terms:
2 + 4y + 10y + -2y2 = -2 + -10y + 2y2 + 2 + 10y + -2y2

Combine like terms: 4y + 10y = 14y
2 + 14y + -2y2 = -2 + -10y + 2y2 + 2 + 10y + -2y2

Reorder the terms:
2 + 14y + -2y2 = -2 + 2 + -10y + 10y + 2y2 + -2y2

Combine like terms: -2 + 2 = 0
2 + 14y + -2y2 = 0 + -10y + 10y + 2y2 + -2y2
2 + 14y + -2y2 = -10y + 10y + 2y2 + -2y2

Combine like terms: -10y + 10y = 0
2 + 14y + -2y2 = 0 + 2y2 + -2y2
2 + 14y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
2 + 14y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 7y + -1y2) = 0

Ignore the factor 2.

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

Simplifying
1 + 7y + -1y2 = 0

Solving
1 + 7y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1 + -7y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + -7y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7y + y2 = 0 + 1
-7y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7y + y2 = 1

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = 1 + 12.25

Reorder the terms:
12.25 + -7y + y2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + -7y + y2 = 13.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(y + -3.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
y + -3.5 = 3.640054945

Simplifying
y + -3.5 = 3.640054945

Reorder the terms:
-3.5 + y = 3.640054945

Solving
-3.5 + y = 3.640054945

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = 3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = 3.640054945 + 3.5
y = 3.640054945 + 3.5

Combine like terms: 3.640054945 + 3.5 = 7.140054945
y = 7.140054945

Simplifying
y = 7.140054945


Subproblem 2
y + -3.5 = -3.640054945

Simplifying
y + -3.5 = -3.640054945

Reorder the terms:
-3.5 + y = -3.640054945

Solving
-3.5 + y = -3.640054945

Solving for variable 'y'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + y = -3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + y = -3.640054945 + 3.5
y = -3.640054945 + 3.5

Combine like terms: -3.640054945 + 3.5 = -0.140054945
y = -0.140054945

Simplifying
y = -0.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.140054945, -0.140054945}
Solution
y = {7.140054945, -0.140054945}

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