12y(3y+1)+3y+1=

Solution for 12y(3y+1)+3y+1= equation:

Simplifying
12y(3y + 1) + 3y + 1 = 0

Reorder the terms:
12y(1 + 3y) + 3y + 1 = 0
(1 * 12y + 3y * 12y) + 3y + 1 = 0
(12y + 36y2) + 3y + 1 = 0

Reorder the terms:
1 + 12y + 3y + 36y2 = 0

Combine like terms: 12y + 3y = 15y
1 + 15y + 36y2 = 0

Solving
1 + 15y + 36y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + 3y)(1 + 12y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 12y)' equal to zero and attempt to solve:

Simplifying
1 + 12y = 0

Solving
1 + 12y = 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 + 12y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12y = 0 + -1
12y = 0 + -1

Combine like terms: 0 + -1 = -1
12y = -1

Divide each side by '12'.
y = -0.08333333333

Simplifying
y = -0.08333333333
Solution
y = {-0.3333333333, -0.08333333333}