(3y+4)(y+8)=20

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Solution for (3y+4)(y+8)=20 equation: 


Simplifying
(3y + 4)(y + 8) = 20

Reorder the terms:
(4 + 3y)(y + 8) = 20

Reorder the terms:
(4 + 3y)(8 + y) = 20

Multiply (4 + 3y) * (8 + y)
(4(8 + y) + 3y * (8 + y)) = 20
((8 * 4 + y * 4) + 3y * (8 + y)) = 20
((32 + 4y) + 3y * (8 + y)) = 20
(32 + 4y + (8 * 3y + y * 3y)) = 20
(32 + 4y + (24y + 3y2)) = 20

Combine like terms: 4y + 24y = 28y
(32 + 28y + 3y2) = 20

Solving
32 + 28y + 3y2 = 20

Solving for variable 'y'.

Reorder the terms:
32 + -20 + 28y + 3y2 = 20 + -20

Combine like terms: 32 + -20 = 12
12 + 28y + 3y2 = 20 + -20

Combine like terms: 20 + -20 = 0
12 + 28y + 3y2 = 0

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

Divide each side by '3'.
4 + 9.333333333y + y2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 9.333333333y + -4 + y2 = 0 + -4

Reorder the terms:
4 + -4 + 9.333333333y + y2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9.333333333y + y2 = 0 + -4
9.333333333y + y2 = 0 + -4

Combine like terms: 0 + -4 = -4
9.333333333y + y2 = -4

The y term is 9.333333333y.  Take half its coefficient (4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
9.333333333y + 21.77777778 + y2 = -4 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333y + y2 = -4 + 21.77777778

Combine like terms: -4 + 21.77777778 = 17.77777778
21.77777778 + 9.333333333y + y2 = 17.77777778

Factor a perfect square on the left side:
(y + 4.666666667)(y + 4.666666667) = 17.77777778

Calculate the square root of the right side: 4.216370214

Break this problem into two subproblems by setting 
(y + 4.666666667) equal to 4.216370214 and -4.216370214.


Subproblem 1
y + 4.666666667 = 4.216370214

Simplifying
y + 4.666666667 = 4.216370214

Reorder the terms:
4.666666667 + y = 4.216370214

Solving
4.666666667 + y = 4.216370214

Solving for variable 'y'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + y = 4.216370214 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + y = 4.216370214 + -4.666666667
y = 4.216370214 + -4.666666667

Combine like terms: 4.216370214 + -4.666666667 = -0.450296453
y = -0.450296453

Simplifying
y = -0.450296453


Subproblem 2
y + 4.666666667 = -4.216370214

Simplifying
y + 4.666666667 = -4.216370214

Reorder the terms:
4.666666667 + y = -4.216370214

Solving
4.666666667 + y = -4.216370214

Solving for variable 'y'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + y = -4.216370214 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + y = -4.216370214 + -4.666666667
y = -4.216370214 + -4.666666667

Combine like terms: -4.216370214 + -4.666666667 = -8.883036881
y = -8.883036881

Simplifying
y = -8.883036881


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.450296453, -8.883036881}

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