6y+8+y(8+y)=180

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Solution for 6y+8+y(8+y)=180 equation: 


Simplifying
6y + 8 + y(8 + y) = 180
6y + 8 + (8 * y + y * y) = 180
6y + 8 + (8y + y2) = 180

Reorder the terms:
8 + 6y + 8y + y2 = 180

Combine like terms: 6y + 8y = 14y
8 + 14y + y2 = 180

Solving
8 + 14y + y2 = 180

Solving for variable 'y'.

Reorder the terms:
8 + -180 + 14y + y2 = 180 + -180

Combine like terms: 8 + -180 = -172
-172 + 14y + y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-172 + 14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '172' to each side of the equation.
-172 + 14y + 172 + y2 = 0 + 172

Reorder the terms:
-172 + 172 + 14y + y2 = 0 + 172

Combine like terms: -172 + 172 = 0
0 + 14y + y2 = 0 + 172
14y + y2 = 0 + 172

Combine like terms: 0 + 172 = 172
14y + y2 = 172

The y term is 14y.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14y + 49 + y2 = 172 + 49

Reorder the terms:
49 + 14y + y2 = 172 + 49

Combine like terms: 172 + 49 = 221
49 + 14y + y2 = 221

Factor a perfect square on the left side:
(y + 7)(y + 7) = 221

Calculate the square root of the right side: 14.866068747

Break this problem into two subproblems by setting 
(y + 7) equal to 14.866068747 and -14.866068747.


Subproblem 1
y + 7 = 14.866068747

Simplifying
y + 7 = 14.866068747

Reorder the terms:
7 + y = 14.866068747

Solving
7 + y = 14.866068747

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = 14.866068747 + -7

Combine like terms: 7 + -7 = 0
0 + y = 14.866068747 + -7
y = 14.866068747 + -7

Combine like terms: 14.866068747 + -7 = 7.866068747
y = 7.866068747

Simplifying
y = 7.866068747


Subproblem 2
y + 7 = -14.866068747

Simplifying
y + 7 = -14.866068747

Reorder the terms:
7 + y = -14.866068747

Solving
7 + y = -14.866068747

Solving for variable 'y'.

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

Add '-7' to each side of the equation.
7 + -7 + y = -14.866068747 + -7

Combine like terms: 7 + -7 = 0
0 + y = -14.866068747 + -7
y = -14.866068747 + -7

Combine like terms: -14.866068747 + -7 = -21.866068747
y = -21.866068747

Simplifying
y = -21.866068747


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.866068747, -21.866068747}

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