(5y-13)(1+y)=0

Solution for (5y-13)(1+y)=0 equation:

Simplifying
(5y + -13)(1 + y) = 0

Reorder the terms:
(-13 + 5y)(1 + y) = 0

Multiply (-13 + 5y) * (1 + y)
(-13(1 + y) + 5y * (1 + y)) = 0
((1 * -13 + y * -13) + 5y * (1 + y)) = 0
((-13 + -13y) + 5y * (1 + y)) = 0
(-13 + -13y + (1 * 5y + y * 5y)) = 0
(-13 + -13y + (5y + 5y2)) = 0

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

Solving
-13 + -8y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -1y)(13 + -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 '(13 + -5y)' equal to zero and attempt to solve:

Simplifying
13 + -5y = 0

Solving
13 + -5y = 0

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

Add '-13' to each side of the equation.
13 + -13 + -5y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -5y = 0 + -13
-5y = 0 + -13

Combine like terms: 0 + -13 = -13
-5y = -13

Divide each side by '-5'.
y = 2.6

Simplifying
y = 2.6
Solution
y = {-1, 2.6}