2(y+6)(y-8)=0

Solution for 2(y+6)(y-8)=0 equation:

Simplifying
2(y + 6)(y + -8) = 0

Reorder the terms:
2(6 + y)(y + -8) = 0

Reorder the terms:
2(6 + y)(-8 + y) = 0

Multiply (6 + y) * (-8 + y)
2(6(-8 + y) + y(-8 + y)) = 0
2((-8 * 6 + y * 6) + y(-8 + y)) = 0
2((-48 + 6y) + y(-8 + y)) = 0
2(-48 + 6y + (-8 * y + y * y)) = 0
2(-48 + 6y + (-8y + y2)) = 0

Combine like terms: 6y + -8y = -2y
2(-48 + -2y + y2) = 0
(-48 * 2 + -2y * 2 + y2 * 2) = 0
(-96 + -4y + 2y2) = 0

Solving
-96 + -4y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + -2y + y2) = 0

Factor a trinomial.
2((-6 + -1y)(8 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-6, 8}