5y(2y+3)=20

Solution for 5y(2y+3)=20 equation:

Simplifying
5y(2y + 3) = 20

Reorder the terms:
5y(3 + 2y) = 20
(3 * 5y + 2y * 5y) = 20
(15y + 10y2) = 20

Solving
15y + 10y2 = 20

Solving for variable 'y'.

Reorder the terms:
-20 + 15y + 10y2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 15y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 3y + 2y2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + 3y + 2y2)' equal to zero and attempt to solve:

Simplifying
-4 + 3y + 2y2 = 0

Solving
-4 + 3y + 2y2 = 0

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

Divide each side by '2'.
-2 + 1.5y + y2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.5y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.5y + y2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.5y + y2 = 0 + 2
1.5y + y2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.5y + y2 = 2

The y term is 1.5y.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5y + 0.5625 + y2 = 2 + 0.5625

Reorder the terms:
0.5625 + 1.5y + y2 = 2 + 0.5625

Combine like terms: 2 + 0.5625 = 2.5625
0.5625 + 1.5y + y2 = 2.5625

Factor a perfect square on the left side:
(y + 0.75)(y + 0.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(y + 0.75) equal to 1.600781059 and -1.600781059.

Subproblem 1
y + 0.75 = 1.600781059

Simplifying
y + 0.75 = 1.600781059

Reorder the terms:
0.75 + y = 1.600781059

Solving
0.75 + y = 1.600781059

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = 1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = 1.600781059 + -0.75
y = 1.600781059 + -0.75

Combine like terms: 1.600781059 + -0.75 = 0.850781059
y = 0.850781059

Simplifying
y = 0.850781059

Subproblem 2
y + 0.75 = -1.600781059

Simplifying
y + 0.75 = -1.600781059

Reorder the terms:
0.75 + y = -1.600781059

Solving
0.75 + y = -1.600781059

Solving for variable 'y'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + y = -1.600781059 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + y = -1.600781059 + -0.75
y = -1.600781059 + -0.75

Combine like terms: -1.600781059 + -0.75 = -2.350781059
y = -2.350781059

Simplifying
y = -2.350781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.850781059, -2.350781059}
Solution
y = {0.850781059, -2.350781059}