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

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

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

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

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

Combine like terms: 5y + -4y = 1y
(-4 + 1y + 5y2) = 0

Solving
-4 + 1y + 5y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-1 + -1y = 0

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

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

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

Divide each side by '-1'.
y = -1

Simplifying
y = -1
Subproblem 2
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5y = 0 + -4

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

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

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Solution
y = {-1, 0.8}