4(10+-2.5y)10y=40

Solution for 4(10+-2.5y)10y=40 equation:

Simplifying
4(10 + -2.5y) * 10y = 40

Reorder the terms for easier multiplication:
4 * 10y(10 + -2.5y) = 40

Multiply 4 * 10
40y(10 + -2.5y) = 40
(10 * 40y + -2.5y * 40y) = 40
(400y + -100y2) = 40

Solving
400y + -100y2 = 40

Solving for variable 'y'.

Reorder the terms:
-40 + 400y + -100y2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 400y + -100y2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-2 + 20y + -5y2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-2 + 20y + -5y2)' equal to zero and attempt to solve:

Simplifying
-2 + 20y + -5y2 = 0

Solving
-2 + 20y + -5y2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.4 + -4y + y2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -4y + -0.4 + y2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -4y + y2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -4y + y2 = 0 + -0.4
-4y + y2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-4y + y2 = -0.4

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -0.4 + 4

Reorder the terms:
4 + -4y + y2 = -0.4 + 4

Combine like terms: -0.4 + 4 = 3.6
4 + -4y + y2 = 3.6

Factor a perfect square on the left side:
(y + -2)(y + -2) = 3.6

Calculate the square root of the right side: 1.897366596

Break this problem into two subproblems by setting 
(y + -2) equal to 1.897366596 and -1.897366596.

Subproblem 1
y + -2 = 1.897366596

Simplifying
y + -2 = 1.897366596

Reorder the terms:
-2 + y = 1.897366596

Solving
-2 + y = 1.897366596

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 1.897366596 + 2

Combine like terms: -2 + 2 = 0
0 + y = 1.897366596 + 2
y = 1.897366596 + 2

Combine like terms: 1.897366596 + 2 = 3.897366596
y = 3.897366596

Simplifying
y = 3.897366596

Subproblem 2
y + -2 = -1.897366596

Simplifying
y + -2 = -1.897366596

Reorder the terms:
-2 + y = -1.897366596

Solving
-2 + y = -1.897366596

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -1.897366596 + 2

Combine like terms: -2 + 2 = 0
0 + y = -1.897366596 + 2
y = -1.897366596 + 2

Combine like terms: -1.897366596 + 2 = 0.102633404
y = 0.102633404

Simplifying
y = 0.102633404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.897366596, 0.102633404}
Solution
y = {3.897366596, 0.102633404}