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

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

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

Reorder the terms:
y(1 + 2y) + -3(2y + 1) = 0
(1 * y + 2y * y) + -3(2y + 1) = 0
(1y + 2y2) + -3(2y + 1) = 0

Reorder the terms:
1y + 2y2 + -3(1 + 2y) = 0
1y + 2y2 + (1 * -3 + 2y * -3) = 0
1y + 2y2 + (-3 + -6y) = 0

Reorder the terms:
-3 + 1y + -6y + 2y2 = 0

Combine like terms: 1y + -6y = -5y
-3 + -5y + 2y2 = 0

Solving
-3 + -5y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -2y)(3 + -1y) = 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 '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

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

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.5, 3}