45=(2y+1)(y-1)

Solution for 45=(2y+1)(y-1) equation:

Simplifying
45 = (2y + 1)(y + -1)

Reorder the terms:
45 = (1 + 2y)(y + -1)

Reorder the terms:
45 = (1 + 2y)(-1 + y)

Multiply (1 + 2y) * (-1 + y)
45 = (1(-1 + y) + 2y * (-1 + y))
45 = ((-1 * 1 + y * 1) + 2y * (-1 + y))
45 = ((-1 + 1y) + 2y * (-1 + y))
45 = (-1 + 1y + (-1 * 2y + y * 2y))
45 = (-1 + 1y + (-2y + 2y2))

Combine like terms: 1y + -2y = -1y
45 = (-1 + -1y + 2y2)

Solving
45 = -1 + -1y + 2y2

Solving for variable 'y'.

Combine like terms: 45 + 1 = 46
46 + y + -2y2 = -1 + -1y + 2y2 + 1 + y + -2y2

Reorder the terms:
46 + y + -2y2 = -1 + 1 + -1y + y + 2y2 + -2y2

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

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

Combine like terms: 2y2 + -2y2 = 0
46 + y + -2y2 = 0

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

Divide each side by '-2'.
-23 + -0.5y + y2 = 0

Move the constant term to the right:

Add '23' to each side of the equation.
-23 + -0.5y + 23 + y2 = 0 + 23

Reorder the terms:
-23 + 23 + -0.5y + y2 = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -0.5y + y2 = 0 + 23
-0.5y + y2 = 0 + 23

Combine like terms: 0 + 23 = 23
-0.5y + y2 = 23

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.5y + 0.25 + y2 = 23 + 0.25

Reorder the terms:
0.25 + -0.5y + y2 = 23 + 0.25

Combine like terms: 23 + 0.25 = 23.25
0.25 + -0.5y + y2 = 23.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(y + 0.5) equal to 4.82182538 and -4.82182538.

Subproblem 1
y + 0.5 = 4.82182538

Simplifying
y + 0.5 = 4.82182538

Reorder the terms:
0.5 + y = 4.82182538

Solving
0.5 + y = 4.82182538

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 4.82182538 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 4.82182538 + -0.5
y = 4.82182538 + -0.5

Combine like terms: 4.82182538 + -0.5 = 4.32182538
y = 4.32182538

Simplifying
y = 4.32182538

Subproblem 2
y + 0.5 = -4.82182538

Simplifying
y + 0.5 = -4.82182538

Reorder the terms:
0.5 + y = -4.82182538

Solving
0.5 + y = -4.82182538

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -4.82182538 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -4.82182538 + -0.5
y = -4.82182538 + -0.5

Combine like terms: -4.82182538 + -0.5 = -5.32182538
y = -5.32182538

Simplifying
y = -5.32182538

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.32182538, -5.32182538}