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

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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 = -3y
45 = (1 + -3y + 2y2)

Solving
45 = 1 + -3y + 2y2

Solving for variable 'y'.

Combine like terms: 45 + -1 = 44
44 + 3y + -2y2 = 1 + -3y + 2y2 + -1 + 3y + -2y2

Reorder the terms:
44 + 3y + -2y2 = 1 + -1 + -3y + 3y + 2y2 + -2y2

Combine like terms: 1 + -1 = 0
44 + 3y + -2y2 = 0 + -3y + 3y + 2y2 + -2y2
44 + 3y + -2y2 = -3y + 3y + 2y2 + -2y2

Combine like terms: -3y + 3y = 0
44 + 3y + -2y2 = 0 + 2y2 + -2y2
44 + 3y + -2y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
44 + 3y + -2y2 = 0

Factor a trinomial.
(11 + -2y)(4 + y) = 0


Subproblem 1
Set the factor '(11 + -2y)' equal to zero and attempt to solve:

Simplifying
11 + -2y = 0

Solving
11 + -2y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2y = 0 + -11
-2y = 0 + -11

Combine like terms: 0 + -11 = -11
-2y = -11

Divide each side by '-2'.
y = 5.5

Simplifying
y = 5.5

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

Solving
4 + y = 0

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

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

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

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

Simplifying
y = -4
Solution
y = {5.5, -4}

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