(2y+1)(y+14)=0

Solution for (2y+1)(y+14)=0 equation:

Simplifying
(2y + 1)(y + 14) = 0

Reorder the terms:
(1 + 2y)(y + 14) = 0

Reorder the terms:
(1 + 2y)(14 + y) = 0

Multiply (1 + 2y) * (14 + y)
(1(14 + y) + 2y * (14 + y)) = 0
((14 * 1 + y * 1) + 2y * (14 + y)) = 0
((14 + 1y) + 2y * (14 + y)) = 0
(14 + 1y + (14 * 2y + y * 2y)) = 0
(14 + 1y + (28y + 2y2)) = 0

Combine like terms: 1y + 28y = 29y
(14 + 29y + 2y2) = 0

Solving
14 + 29y + 2y2 = 0

Solving for variable 'y'.

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

Subproblem 1
Set the factor '(14 + y)' equal to zero and attempt to solve:

Simplifying
14 + y = 0

Solving
14 + y = 0

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

Add '-14' to each side of the equation.
14 + -14 + y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + y = 0 + -14
y = 0 + -14

Combine like terms: 0 + -14 = -14
y = -14

Simplifying
y = -14
Subproblem 2
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
Solution
y = {-14, -0.5}