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

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

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

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

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

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

Combine like terms: 1y + -5y = -4y
2(-5 + -4y + y2) = 0
(-5 * 2 + -4y * 2 + y2 * 2) = 0
(-10 + -8y + 2y2) = 0

Solving
-10 + -8y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -4y + y2) = 0

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

Ignore the factor 2.
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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

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

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

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

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-1, 5}