(2y-14)(y+1)=-6y+1

Solution for (2y-14)(y+1)=-6y+1 equation:

Simplifying
(2y + -14)(y + 1) = -6y + 1

Reorder the terms:
(-14 + 2y)(y + 1) = -6y + 1

Reorder the terms:
(-14 + 2y)(1 + y) = -6y + 1

Multiply (-14 + 2y) * (1 + y)
(-14(1 + y) + 2y * (1 + y)) = -6y + 1
((1 * -14 + y * -14) + 2y * (1 + y)) = -6y + 1
((-14 + -14y) + 2y * (1 + y)) = -6y + 1
(-14 + -14y + (1 * 2y + y * 2y)) = -6y + 1
(-14 + -14y + (2y + 2y2)) = -6y + 1

Combine like terms: -14y + 2y = -12y
(-14 + -12y + 2y2) = -6y + 1

Reorder the terms:
-14 + -12y + 2y2 = 1 + -6y

Solving
-14 + -12y + 2y2 = 1 + -6y

Solving for variable 'y'.

Reorder the terms:
-14 + -1 + -12y + 6y + 2y2 = 1 + -6y + -1 + 6y

Combine like terms: -14 + -1 = -15
-15 + -12y + 6y + 2y2 = 1 + -6y + -1 + 6y

Combine like terms: -12y + 6y = -6y
-15 + -6y + 2y2 = 1 + -6y + -1 + 6y

Reorder the terms:
-15 + -6y + 2y2 = 1 + -1 + -6y + 6y

Combine like terms: 1 + -1 = 0
-15 + -6y + 2y2 = 0 + -6y + 6y
-15 + -6y + 2y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
-15 + -6y + 2y2 = 0

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

Divide each side by '2'.
-7.5 + -3y + y2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3y + 7.5 + y2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3y + y2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3y + y2 = 0 + 7.5
-3y + y2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-3y + y2 = 7.5

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 7.5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + -3y + y2 = 9.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(y + -1.5) equal to 3.122498999 and -3.122498999.

Subproblem 1
y + -1.5 = 3.122498999

Simplifying
y + -1.5 = 3.122498999

Reorder the terms:
-1.5 + y = 3.122498999

Solving
-1.5 + y = 3.122498999

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 3.122498999 + 1.5
y = 3.122498999 + 1.5

Combine like terms: 3.122498999 + 1.5 = 4.622498999
y = 4.622498999

Simplifying
y = 4.622498999

Subproblem 2
y + -1.5 = -3.122498999

Simplifying
y + -1.5 = -3.122498999

Reorder the terms:
-1.5 + y = -3.122498999

Solving
-1.5 + y = -3.122498999

Solving for variable 'y'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -3.122498999 + 1.5
y = -3.122498999 + 1.5

Combine like terms: -3.122498999 + 1.5 = -1.622498999
y = -1.622498999

Simplifying
y = -1.622498999

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.622498999, -1.622498999}