8y(5y+2)=16

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Solution for 8y(5y+2)=16 equation: 


Simplifying
8y(5y + 2) = 16

Reorder the terms:
8y(2 + 5y) = 16
(2 * 8y + 5y * 8y) = 16
(16y + 40y2) = 16

Solving
16y + 40y2 = 16

Solving for variable 'y'.

Reorder the terms:
-16 + 16y + 40y2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 16y + 40y2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + 2y + 5y2) = 0

Ignore the factor 8.

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

Simplifying
-2 + 2y + 5y2 = 0

Solving
-2 + 2y + 5y2 = 0

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

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

Move the constant term to the right:

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

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

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

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

The y term is 0.4y.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4y + 0.04 + y2 = 0.4 + 0.04

Reorder the terms:
0.04 + 0.4y + y2 = 0.4 + 0.04

Combine like terms: 0.4 + 0.04 = 0.44
0.04 + 0.4y + y2 = 0.44

Factor a perfect square on the left side:
(y + 0.2)(y + 0.2) = 0.44

Calculate the square root of the right side: 0.663324958

Break this problem into two subproblems by setting 
(y + 0.2) equal to 0.663324958 and -0.663324958.


Subproblem 1
y + 0.2 = 0.663324958

Simplifying
y + 0.2 = 0.663324958

Reorder the terms:
0.2 + y = 0.663324958

Solving
0.2 + y = 0.663324958

Solving for variable 'y'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + y = 0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + y = 0.663324958 + -0.2
y = 0.663324958 + -0.2

Combine like terms: 0.663324958 + -0.2 = 0.463324958
y = 0.463324958

Simplifying
y = 0.463324958


Subproblem 2
y + 0.2 = -0.663324958

Simplifying
y + 0.2 = -0.663324958

Reorder the terms:
0.2 + y = -0.663324958

Solving
0.2 + y = -0.663324958

Solving for variable 'y'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + y = -0.663324958 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + y = -0.663324958 + -0.2
y = -0.663324958 + -0.2

Combine like terms: -0.663324958 + -0.2 = -0.863324958
y = -0.863324958

Simplifying
y = -0.863324958


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.463324958, -0.863324958}
Solution
y = {0.463324958, -0.863324958}

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