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

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

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

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

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

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

Solving
-2 + 9y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(1 + -5y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

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

Simplifying
1 + -5y = 0

Solving
1 + -5y = 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 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {-2, 0.2}