(y-6)(y+1)=4

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Solution for (y-6)(y+1)=4 equation: 


Simplifying
(y + -6)(y + 1) = 4

Reorder the terms:
(-6 + y)(y + 1) = 4

Reorder the terms:
(-6 + y)(1 + y) = 4

Multiply (-6 + y) * (1 + y)
(-6(1 + y) + y(1 + y)) = 4
((1 * -6 + y * -6) + y(1 + y)) = 4
((-6 + -6y) + y(1 + y)) = 4
(-6 + -6y + (1 * y + y * y)) = 4
(-6 + -6y + (1y + y2)) = 4

Combine like terms: -6y + 1y = -5y
(-6 + -5y + y2) = 4

Solving
-6 + -5y + y2 = 4

Solving for variable 'y'.

Reorder the terms:
-6 + -4 + -5y + y2 = 4 + -4

Combine like terms: -6 + -4 = -10
-10 + -5y + y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-10 + -5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -5y + 10 + y2 = 0 + 10

Reorder the terms:
-10 + 10 + -5y + y2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -5y + y2 = 0 + 10
-5y + y2 = 0 + 10

Combine like terms: 0 + 10 = 10
-5y + y2 = 10

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 = 10 + 6.25

Reorder the terms:
6.25 + -5y + y2 = 10 + 6.25

Combine like terms: 10 + 6.25 = 16.25
6.25 + -5y + y2 = 16.25

Factor a perfect square on the left side:
(y + -2.5)(y + -2.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(y + -2.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
y + -2.5 = 4.031128874

Simplifying
y + -2.5 = 4.031128874

Reorder the terms:
-2.5 + y = 4.031128874

Solving
-2.5 + y = 4.031128874

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 = 4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = 4.031128874 + 2.5
y = 4.031128874 + 2.5

Combine like terms: 4.031128874 + 2.5 = 6.531128874
y = 6.531128874

Simplifying
y = 6.531128874


Subproblem 2
y + -2.5 = -4.031128874

Simplifying
y + -2.5 = -4.031128874

Reorder the terms:
-2.5 + y = -4.031128874

Solving
-2.5 + y = -4.031128874

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 = -4.031128874 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + y = -4.031128874 + 2.5
y = -4.031128874 + 2.5

Combine like terms: -4.031128874 + 2.5 = -1.531128874
y = -1.531128874

Simplifying
y = -1.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.531128874, -1.531128874}

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