(4y+2)*(5y)=130

Solution for (4y+2)*(5y)=130 equation:

Simplifying
(4y + 2)(5y) = 130

Reorder the terms:
(2 + 4y)(5y) = 130

Remove parenthesis around (5y)
(2 + 4y) * 5y = 130

Reorder the terms for easier multiplication:
5y(2 + 4y) = 130
(2 * 5y + 4y * 5y) = 130
(10y + 20y2) = 130

Solving
10y + 20y2 = 130

Solving for variable 'y'.

Reorder the terms:
-130 + 10y + 20y2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 10y + 20y2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-13 + y + 2y2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-13 + y + 2y2)' equal to zero and attempt to solve:

Simplifying
-13 + y + 2y2 = 0

Solving
-13 + y + 2y2 = 0

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

Divide each side by '2'.
-6.5 + 0.5y + y2 = 0

Move the constant term to the right:

Add '6.5' to each side of the equation.
-6.5 + 0.5y + 6.5 + y2 = 0 + 6.5

Reorder the terms:
-6.5 + 6.5 + 0.5y + y2 = 0 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + 0.5y + y2 = 0 + 6.5
0.5y + y2 = 0 + 6.5

Combine like terms: 0 + 6.5 = 6.5
0.5y + y2 = 6.5

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5y + 0.25 + y2 = 6.5 + 0.25

Reorder the terms:
0.25 + 0.5y + y2 = 6.5 + 0.25

Combine like terms: 6.5 + 0.25 = 6.75
0.25 + 0.5y + y2 = 6.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 6.75

Calculate the square root of the right side: 2.598076211

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.598076211 and -2.598076211.

Subproblem 1
y + 0.5 = 2.598076211

Simplifying
y + 0.5 = 2.598076211

Reorder the terms:
0.5 + y = 2.598076211

Solving
0.5 + y = 2.598076211

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 2.598076211 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.598076211 + -0.5
y = 2.598076211 + -0.5

Combine like terms: 2.598076211 + -0.5 = 2.098076211
y = 2.098076211

Simplifying
y = 2.098076211

Subproblem 2
y + 0.5 = -2.598076211

Simplifying
y + 0.5 = -2.598076211

Reorder the terms:
0.5 + y = -2.598076211

Solving
0.5 + y = -2.598076211

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -2.598076211 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.598076211 + -0.5
y = -2.598076211 + -0.5

Combine like terms: -2.598076211 + -0.5 = -3.098076211
y = -3.098076211

Simplifying
y = -3.098076211

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.098076211, -3.098076211}
Solution
y = {2.098076211, -3.098076211}