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

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

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

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

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

Combine like terms: 2y + 5y = 7y
(2 + 7y + 5y2) = 0

Solving
2 + 7y + 5y2 = 0

Solving for variable 'y'.

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

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

Simplifying
2 + 5y = 0

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

Combine like terms: 2 + -2 = 0
0 + 5y = 0 + -2
5y = 0 + -2

Combine like terms: 0 + -2 = -2
5y = -2

Divide each side by '5'.
y = -0.4

Simplifying
y = -0.4
Solution
y = {-1, -0.4}