(8-4y)-y(2y+6)=

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Solution for (8-4y)-y(2y+6)= equation: 


Simplifying
(8 + -4y) + -1y(2y + 6) = 0

Remove parenthesis around (8 + -4y)
8 + -4y + -1y(2y + 6) = 0

Reorder the terms:
8 + -4y + -1y(6 + 2y) = 0
8 + -4y + (6 * -1y + 2y * -1y) = 0
8 + -4y + (-6y + -2y2) = 0

Combine like terms: -4y + -6y = -10y
8 + -10y + -2y2 = 0

Solving
8 + -10y + -2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -5y + -1y2) = 0

Ignore the factor 2.

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

Simplifying
4 + -5y + -1y2 = 0

Solving
4 + -5y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 5y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 5y + y2 = 0 + 4
5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
5y + y2 = 4

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 4 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 4 + 6.25

Combine like terms: 4 + 6.25 = 10.25
6.25 + 5y + y2 = 10.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(y + 2.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
y + 2.5 = 3.201562119

Simplifying
y + 2.5 = 3.201562119

Reorder the terms:
2.5 + y = 3.201562119

Solving
2.5 + y = 3.201562119

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 3.201562119 + -2.5
y = 3.201562119 + -2.5

Combine like terms: 3.201562119 + -2.5 = 0.701562119
y = 0.701562119

Simplifying
y = 0.701562119


Subproblem 2
y + 2.5 = -3.201562119

Simplifying
y + 2.5 = -3.201562119

Reorder the terms:
2.5 + y = -3.201562119

Solving
2.5 + y = -3.201562119

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -3.201562119 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -3.201562119 + -2.5
y = -3.201562119 + -2.5

Combine like terms: -3.201562119 + -2.5 = -5.701562119
y = -5.701562119

Simplifying
y = -5.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.701562119, -5.701562119}
Solution
y = {0.701562119, -5.701562119}

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