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

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


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

Combine like terms: 2y + -4y = -2y
5y + -4y(-2y) = 2

Remove parenthesis around (-2y)
5y + -4y * -2y = 2

Reorder the terms for easier multiplication:
5y + -4 * -2y * y = 2

Multiply -4 * -2
5y + 8y * y = 2

Multiply y * y
5y + 8y2 = 2

Solving
5y + 8y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 5y + 8y2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 5y + 8y2 = 0

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

Divide each side by '8'.
-0.25 + 0.625y + y2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 0.625y + 0.25 + y2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 0.625y + y2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 0.625y + y2 = 0 + 0.25
0.625y + y2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
0.625y + y2 = 0.25

The y term is 0.625y.  Take half its coefficient (0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
0.625y + 0.09765625 + y2 = 0.25 + 0.09765625

Reorder the terms:
0.09765625 + 0.625y + y2 = 0.25 + 0.09765625

Combine like terms: 0.25 + 0.09765625 = 0.34765625
0.09765625 + 0.625y + y2 = 0.34765625

Factor a perfect square on the left side:
(y + 0.3125)(y + 0.3125) = 0.34765625

Calculate the square root of the right side: 0.589623821

Break this problem into two subproblems by setting 
(y + 0.3125) equal to 0.589623821 and -0.589623821.


Subproblem 1
y + 0.3125 = 0.589623821

Simplifying
y + 0.3125 = 0.589623821

Reorder the terms:
0.3125 + y = 0.589623821

Solving
0.3125 + y = 0.589623821

Solving for variable 'y'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + y = 0.589623821 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + y = 0.589623821 + -0.3125
y = 0.589623821 + -0.3125

Combine like terms: 0.589623821 + -0.3125 = 0.277123821
y = 0.277123821

Simplifying
y = 0.277123821


Subproblem 2
y + 0.3125 = -0.589623821

Simplifying
y + 0.3125 = -0.589623821

Reorder the terms:
0.3125 + y = -0.589623821

Solving
0.3125 + y = -0.589623821

Solving for variable 'y'.

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

Add '-0.3125' to each side of the equation.
0.3125 + -0.3125 + y = -0.589623821 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + y = -0.589623821 + -0.3125
y = -0.589623821 + -0.3125

Combine like terms: -0.589623821 + -0.3125 = -0.902123821
y = -0.902123821

Simplifying
y = -0.902123821


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.277123821, -0.902123821}

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