4y(5y-2)=122

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Solution for 4y(5y-2)=122 equation: 


Simplifying
4y(5y + -2) = 122

Reorder the terms:
4y(-2 + 5y) = 122
(-2 * 4y + 5y * 4y) = 122
(-8y + 20y2) = 122

Solving
-8y + 20y2 = 122

Solving for variable 'y'.

Reorder the terms:
-122 + -8y + 20y2 = 122 + -122

Combine like terms: 122 + -122 = 0
-122 + -8y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-61 + -4y + 10y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-61 + -4y + 10y2)' equal to zero and attempt to solve:

Simplifying
-61 + -4y + 10y2 = 0

Solving
-61 + -4y + 10y2 = 0

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

Divide each side by '10'.
-6.1 + -0.4y + y2 = 0.0

Move the constant term to the right:

Add '6.1' to each side of the equation.
-6.1 + -0.4y + 6.1 + y2 = 0.0 + 6.1

Reorder the terms:
-6.1 + 6.1 + -0.4y + y2 = 0.0 + 6.1

Combine like terms: -6.1 + 6.1 = 0.0
0.0 + -0.4y + y2 = 0.0 + 6.1
-0.4y + y2 = 0.0 + 6.1

Combine like terms: 0.0 + 6.1 = 6.1
-0.4y + y2 = 6.1

The y term is -0.4y.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4y + 0.04 + y2 = 6.1 + 0.04

Reorder the terms:
0.04 + -0.4y + y2 = 6.1 + 0.04

Combine like terms: 6.1 + 0.04 = 6.14
0.04 + -0.4y + y2 = 6.14

Factor a perfect square on the left side:
(y + -0.2)(y + -0.2) = 6.14

Calculate the square root of the right side: 2.477902339

Break this problem into two subproblems by setting 
(y + -0.2) equal to 2.477902339 and -2.477902339.


Subproblem 1
y + -0.2 = 2.477902339

Simplifying
y + -0.2 = 2.477902339

Reorder the terms:
-0.2 + y = 2.477902339

Solving
-0.2 + y = 2.477902339

Solving for variable 'y'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + y = 2.477902339 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = 2.477902339 + 0.2
y = 2.477902339 + 0.2

Combine like terms: 2.477902339 + 0.2 = 2.677902339
y = 2.677902339

Simplifying
y = 2.677902339


Subproblem 2
y + -0.2 = -2.477902339

Simplifying
y + -0.2 = -2.477902339

Reorder the terms:
-0.2 + y = -2.477902339

Solving
-0.2 + y = -2.477902339

Solving for variable 'y'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + y = -2.477902339 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + y = -2.477902339 + 0.2
y = -2.477902339 + 0.2

Combine like terms: -2.477902339 + 0.2 = -2.277902339
y = -2.277902339

Simplifying
y = -2.277902339


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.677902339, -2.277902339}
Solution
y = {2.677902339, -2.277902339}

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