(1+y)(5y+8)=0

Solution for (1+y)(5y+8)=0 equation:

Simplifying
(1 + y)(5y + 8) = 0

Reorder the terms:
(1 + y)(8 + 5y) = 0

Multiply (1 + y) * (8 + 5y)
(1(8 + 5y) + y(8 + 5y)) = 0
((8 * 1 + 5y * 1) + y(8 + 5y)) = 0
((8 + 5y) + y(8 + 5y)) = 0
(8 + 5y + (8 * y + 5y * y)) = 0
(8 + 5y + (8y + 5y2)) = 0

Combine like terms: 5y + 8y = 13y
(8 + 13y + 5y2) = 0

Solving
8 + 13y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + 5y)(1 + y) = 0

Subproblem 1
Set the factor '(8 + 5y)' equal to zero and attempt to solve:

Simplifying
8 + 5y = 0

Solving
8 + 5y = 0

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

Add '-8' to each side of the equation.
8 + -8 + 5y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5y = 0 + -8
5y = 0 + -8

Combine like terms: 0 + -8 = -8
5y = -8

Divide each side by '5'.
y = -1.6

Simplifying
y = -1.6
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {-1.6, -1}