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

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

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

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

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

Multiply (1 + 2y) * (-2 + 3y)
(1(-2 + 3y) + 2y * (-2 + 3y)) = 0
((-2 * 1 + 3y * 1) + 2y * (-2 + 3y)) = 0
((-2 + 3y) + 2y * (-2 + 3y)) = 0
(-2 + 3y + (-2 * 2y + 3y * 2y)) = 0
(-2 + 3y + (-4y + 6y2)) = 0

Combine like terms: 3y + -4y = -1y
(-2 + -1y + 6y2) = 0

Solving
-2 + -1y + 6y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-1 + -2y = 0

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

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

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

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 2
Set the factor '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 0

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

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

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-0.5, 0.6666666667}