5y(2y-1)-2(2y)=10

Solution for 5y(2y-1)-2(2y)=10 equation:

Simplifying
5y(2y + -1) + -2(2y) = 10

Reorder the terms:
5y(-1 + 2y) + -2(2y) = 10
(-1 * 5y + 2y * 5y) + -2(2y) = 10
(-5y + 10y2) + -2(2y) = 10

Remove parenthesis around (2y)
-5y + 10y2 + -2 * 2y = 10

Multiply -2 * 2
-5y + 10y2 + -4y = 10

Reorder the terms:
-5y + -4y + 10y2 = 10

Combine like terms: -5y + -4y = -9y
-9y + 10y2 = 10

Solving
-9y + 10y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + -9y + 10y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -9y + 10y2 = 0

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

Divide each side by '10'.
-1 + -0.9y + y2 = 0.0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -0.9y + 1 + y2 = 0.0 + 1

Reorder the terms:
-1 + 1 + -0.9y + y2 = 0.0 + 1

Combine like terms: -1 + 1 = 0
0 + -0.9y + y2 = 0.0 + 1
-0.9y + y2 = 0.0 + 1

Combine like terms: 0.0 + 1 = 1
-0.9y + y2 = 1

The y term is -0.9y.  Take half its coefficient (-0.45).
Square it (0.2025) and add it to both sides.

Add '0.2025' to each side of the equation.
-0.9y + 0.2025 + y2 = 1 + 0.2025

Reorder the terms:
0.2025 + -0.9y + y2 = 1 + 0.2025

Combine like terms: 1 + 0.2025 = 1.2025
0.2025 + -0.9y + y2 = 1.2025

Factor a perfect square on the left side:
(y + -0.45)(y + -0.45) = 1.2025

Calculate the square root of the right side: 1.09658561

Break this problem into two subproblems by setting 
(y + -0.45) equal to 1.09658561 and -1.09658561.

Subproblem 1
y + -0.45 = 1.09658561

Simplifying
y + -0.45 = 1.09658561

Reorder the terms:
-0.45 + y = 1.09658561

Solving
-0.45 + y = 1.09658561

Solving for variable 'y'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + y = 1.09658561 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + y = 1.09658561 + 0.45
y = 1.09658561 + 0.45

Combine like terms: 1.09658561 + 0.45 = 1.54658561
y = 1.54658561

Simplifying
y = 1.54658561

Subproblem 2
y + -0.45 = -1.09658561

Simplifying
y + -0.45 = -1.09658561

Reorder the terms:
-0.45 + y = -1.09658561

Solving
-0.45 + y = -1.09658561

Solving for variable 'y'.

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

Add '0.45' to each side of the equation.
-0.45 + 0.45 + y = -1.09658561 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + y = -1.09658561 + 0.45
y = -1.09658561 + 0.45

Combine like terms: -1.09658561 + 0.45 = -0.64658561
y = -0.64658561

Simplifying
y = -0.64658561

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.54658561, -0.64658561}