5y(8y+13)=6(13+7)

Solution for 5y(8y+13)=6(13+7) equation:

Simplifying
5y(8y + 13) = 6(13 + 7)

Reorder the terms:
5y(13 + 8y) = 6(13 + 7)
(13 * 5y + 8y * 5y) = 6(13 + 7)
(65y + 40y2) = 6(13 + 7)

Combine like terms: 13 + 7 = 20
65y + 40y2 = 6(20)

Multiply 6 * 20
65y + 40y2 = 120

Solving
65y + 40y2 = 120

Solving for variable 'y'.

Reorder the terms:
-120 + 65y + 40y2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 65y + 40y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-24 + 13y + 8y2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-24 + 13y + 8y2)' equal to zero and attempt to solve:

Simplifying
-24 + 13y + 8y2 = 0

Solving
-24 + 13y + 8y2 = 0

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

Divide each side by '8'.
-3 + 1.625y + y2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 1.625y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + 1.625y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 1.625y + y2 = 0 + 3
1.625y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
1.625y + y2 = 3

The y term is 1.625y.  Take half its coefficient (0.8125).
Square it (0.66015625) and add it to both sides.

Add '0.66015625' to each side of the equation.
1.625y + 0.66015625 + y2 = 3 + 0.66015625

Reorder the terms:
0.66015625 + 1.625y + y2 = 3 + 0.66015625

Combine like terms: 3 + 0.66015625 = 3.66015625
0.66015625 + 1.625y + y2 = 3.66015625

Factor a perfect square on the left side:
(y + 0.8125)(y + 0.8125) = 3.66015625

Calculate the square root of the right side: 1.913153483

Break this problem into two subproblems by setting 
(y + 0.8125) equal to 1.913153483 and -1.913153483.

Subproblem 1
y + 0.8125 = 1.913153483

Simplifying
y + 0.8125 = 1.913153483

Reorder the terms:
0.8125 + y = 1.913153483

Solving
0.8125 + y = 1.913153483

Solving for variable 'y'.

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

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + y = 1.913153483 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + y = 1.913153483 + -0.8125
y = 1.913153483 + -0.8125

Combine like terms: 1.913153483 + -0.8125 = 1.100653483
y = 1.100653483

Simplifying
y = 1.100653483

Subproblem 2
y + 0.8125 = -1.913153483

Simplifying
y + 0.8125 = -1.913153483

Reorder the terms:
0.8125 + y = -1.913153483

Solving
0.8125 + y = -1.913153483

Solving for variable 'y'.

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

Add '-0.8125' to each side of the equation.
0.8125 + -0.8125 + y = -1.913153483 + -0.8125

Combine like terms: 0.8125 + -0.8125 = 0.0000
0.0000 + y = -1.913153483 + -0.8125
y = -1.913153483 + -0.8125

Combine like terms: -1.913153483 + -0.8125 = -2.725653483
y = -2.725653483

Simplifying
y = -2.725653483

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.100653483, -2.725653483}
Solution
y = {1.100653483, -2.725653483}