2(y-3)(-y+8)=0

Solution for 2(y-3)(-y+8)=0 equation:

Simplifying
2(y + -3)(-1y + 8) = 0

Reorder the terms:
2(-3 + y)(-1y + 8) = 0

Reorder the terms:
2(-3 + y)(8 + -1y) = 0

Multiply (-3 + y) * (8 + -1y)
2(-3(8 + -1y) + y(8 + -1y)) = 0
2((8 * -3 + -1y * -3) + y(8 + -1y)) = 0
2((-24 + 3y) + y(8 + -1y)) = 0
2(-24 + 3y + (8 * y + -1y * y)) = 0
2(-24 + 3y + (8y + -1y2)) = 0

Combine like terms: 3y + 8y = 11y
2(-24 + 11y + -1y2) = 0
(-24 * 2 + 11y * 2 + -1y2 * 2) = 0
(-48 + 22y + -2y2) = 0

Solving
-48 + 22y + -2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + 11y + -1y2) = 0

Factor a trinomial.
2((-8 + y)(3 + -1y)) = 0

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

Simplifying
-8 + y = 0

Solving
-8 + y = 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 + y = 0 + 8

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

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

Simplifying
y = 8
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {8, 3}