12y(y+2)+5=2y-1

Solution for 12y(y+2)+5=2y-1 equation:

Simplifying
12y(y + 2) + 5 = 2y + -1

Reorder the terms:
12y(2 + y) + 5 = 2y + -1
(2 * 12y + y * 12y) + 5 = 2y + -1
(24y + 12y2) + 5 = 2y + -1

Reorder the terms:
5 + 24y + 12y2 = 2y + -1

Reorder the terms:
5 + 24y + 12y2 = -1 + 2y

Solving
5 + 24y + 12y2 = -1 + 2y

Solving for variable 'y'.

Reorder the terms:
5 + 1 + 24y + -2y + 12y2 = -1 + 2y + 1 + -2y

Combine like terms: 5 + 1 = 6
6 + 24y + -2y + 12y2 = -1 + 2y + 1 + -2y

Combine like terms: 24y + -2y = 22y
6 + 22y + 12y2 = -1 + 2y + 1 + -2y

Reorder the terms:
6 + 22y + 12y2 = -1 + 1 + 2y + -2y

Combine like terms: -1 + 1 = 0
6 + 22y + 12y2 = 0 + 2y + -2y
6 + 22y + 12y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
6 + 22y + 12y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 11y + 6y2) = 0

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

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

Simplifying
1 + 3y = 0

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

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

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

Divide each side by '3'.
y = -0.3333333333

Simplifying
y = -0.3333333333
Solution
y = {-1.5, -0.3333333333}