24y^2+14y+1=0

Solution for 24y^2+14y+1=0 equation:

Simplifying
24y2 + 14y + 1 = 0

Reorder the terms:
1 + 14y + 24y2 = 0

Solving
1 + 14y + 24y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + 2y)(1 + 12y) = 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 '(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 = {-0.5, -0.08333333333}