(1+y)(4y+5)=0

Solution for (1+y)(4y+5)=0 equation:

Simplifying
(1 + y)(4y + 5) = 0

Reorder the terms:
(1 + y)(5 + 4y) = 0

Multiply (1 + y) * (5 + 4y)
(1(5 + 4y) + y(5 + 4y)) = 0
((5 * 1 + 4y * 1) + y(5 + 4y)) = 0
((5 + 4y) + y(5 + 4y)) = 0
(5 + 4y + (5 * y + 4y * y)) = 0
(5 + 4y + (5y + 4y2)) = 0

Combine like terms: 4y + 5y = 9y
(5 + 9y + 4y2) = 0

Solving
5 + 9y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + 4y)(1 + y) = 0

Subproblem 1
Set the factor '(5 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 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 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Divide each side by '4'.
y = -1.25

Simplifying
y = -1.25
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 = {-1.25, -1}