(y+6)(y-2)=7

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Solution for (y+6)(y-2)=7 equation: 


Simplifying
(y + 6)(y + -2) = 7

Reorder the terms:
(6 + y)(y + -2) = 7

Reorder the terms:
(6 + y)(-2 + y) = 7

Multiply (6 + y) * (-2 + y)
(6(-2 + y) + y(-2 + y)) = 7
((-2 * 6 + y * 6) + y(-2 + y)) = 7
((-12 + 6y) + y(-2 + y)) = 7
(-12 + 6y + (-2 * y + y * y)) = 7
(-12 + 6y + (-2y + y2)) = 7

Combine like terms: 6y + -2y = 4y
(-12 + 4y + y2) = 7

Solving
-12 + 4y + y2 = 7

Solving for variable 'y'.

Reorder the terms:
-12 + -7 + 4y + y2 = 7 + -7

Combine like terms: -12 + -7 = -19
-19 + 4y + y2 = 7 + -7

Combine like terms: 7 + -7 = 0
-19 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 4y + 19 + y2 = 0 + 19

Reorder the terms:
-19 + 19 + 4y + y2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 4y + y2 = 0 + 19
4y + y2 = 0 + 19

Combine like terms: 0 + 19 = 19
4y + y2 = 19

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 19 + 4

Reorder the terms:
4 + 4y + y2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + 4y + y2 = 23

Factor a perfect square on the left side:
(y + 2)(y + 2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(y + 2) equal to 4.795831523 and -4.795831523.


Subproblem 1
y + 2 = 4.795831523

Simplifying
y + 2 = 4.795831523

Reorder the terms:
2 + y = 4.795831523

Solving
2 + y = 4.795831523

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 4.795831523 + -2

Combine like terms: 2 + -2 = 0
0 + y = 4.795831523 + -2
y = 4.795831523 + -2

Combine like terms: 4.795831523 + -2 = 2.795831523
y = 2.795831523

Simplifying
y = 2.795831523


Subproblem 2
y + 2 = -4.795831523

Simplifying
y + 2 = -4.795831523

Reorder the terms:
2 + y = -4.795831523

Solving
2 + y = -4.795831523

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -4.795831523 + -2

Combine like terms: 2 + -2 = 0
0 + y = -4.795831523 + -2
y = -4.795831523 + -2

Combine like terms: -4.795831523 + -2 = -6.795831523
y = -6.795831523

Simplifying
y = -6.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.795831523, -6.795831523}

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