(-2y+1)(y+5)=0

Solution for (-2y+1)(y+5)=0 equation:

Simplifying
(-2y + 1)(y + 5) = 0

Reorder the terms:
(1 + -2y)(y + 5) = 0

Reorder the terms:
(1 + -2y)(5 + y) = 0

Multiply (1 + -2y) * (5 + y)
(1(5 + y) + -2y * (5 + y)) = 0
((5 * 1 + y * 1) + -2y * (5 + y)) = 0
((5 + 1y) + -2y * (5 + y)) = 0
(5 + 1y + (5 * -2y + y * -2y)) = 0
(5 + 1y + (-10y + -2y2)) = 0

Combine like terms: 1y + -10y = -9y
(5 + -9y + -2y2) = 0

Solving
5 + -9y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -2y)(5 + y) = 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 '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
Solution
y = {0.5, -5}