(2y-3)(y+1)=0

Solution for (2y-3)(y+1)=0 equation:

Simplifying
(2y + -3)(y + 1) = 0

Reorder the terms:
(-3 + 2y)(y + 1) = 0

Reorder the terms:
(-3 + 2y)(1 + y) = 0

Multiply (-3 + 2y) * (1 + y)
(-3(1 + y) + 2y * (1 + y)) = 0
((1 * -3 + y * -3) + 2y * (1 + y)) = 0
((-3 + -3y) + 2y * (1 + y)) = 0
(-3 + -3y + (1 * 2y + y * 2y)) = 0
(-3 + -3y + (2y + 2y2)) = 0

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

Solving
-3 + -1y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(3 + -2y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2y)' equal to zero and attempt to solve:

Simplifying
3 + -2y = 0

Solving
3 + -2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2y = 0 + -3

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

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

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Solution
y = {-1, 1.5}