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

Solution for (2y-1)(y+1)=(y-3)(y-2) equation:

Simplifying
(2y + -1)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-1 + 2y)(y + 1) = (y + -3)(y + -2)

Reorder the terms:
(-1 + 2y)(1 + y) = (y + -3)(y + -2)

Multiply (-1 + 2y) * (1 + y)
(-1(1 + y) + 2y * (1 + y)) = (y + -3)(y + -2)
((1 * -1 + y * -1) + 2y * (1 + y)) = (y + -3)(y + -2)
((-1 + -1y) + 2y * (1 + y)) = (y + -3)(y + -2)
(-1 + -1y + (1 * 2y + y * 2y)) = (y + -3)(y + -2)
(-1 + -1y + (2y + 2y2)) = (y + -3)(y + -2)

Combine like terms: -1y + 2y = 1y
(-1 + 1y + 2y2) = (y + -3)(y + -2)

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

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

Multiply (-3 + y) * (-2 + y)
-1 + 1y + 2y2 = (-3(-2 + y) + y(-2 + y))
-1 + 1y + 2y2 = ((-2 * -3 + y * -3) + y(-2 + y))
-1 + 1y + 2y2 = ((6 + -3y) + y(-2 + y))
-1 + 1y + 2y2 = (6 + -3y + (-2 * y + y * y))
-1 + 1y + 2y2 = (6 + -3y + (-2y + y2))

Combine like terms: -3y + -2y = -5y
-1 + 1y + 2y2 = (6 + -5y + y2)

Solving
-1 + 1y + 2y2 = 6 + -5y + y2

Solving for variable 'y'.

Reorder the terms:
-1 + -6 + 1y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: -1 + -6 = -7
-7 + 1y + 5y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: 1y + 5y = 6y
-7 + 6y + 2y2 + -1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-7 + 6y + 1y2 = 6 + -5y + y2 + -6 + 5y + -1y2

Reorder the terms:
-7 + 6y + 1y2 = 6 + -6 + -5y + 5y + y2 + -1y2

Combine like terms: 6 + -6 = 0
-7 + 6y + 1y2 = 0 + -5y + 5y + y2 + -1y2
-7 + 6y + 1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
-7 + 6y + 1y2 = 0 + y2 + -1y2
-7 + 6y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-7 + 6y + 1y2 = 0

Factor a trinomial.
(-7 + -1y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Solution
y = {-7, 1}