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

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

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

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

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

Multiply (3 + w) * (-8 + -1w)
2(3(-8 + -1w) + w(-8 + -1w)) = 0
2((-8 * 3 + -1w * 3) + w(-8 + -1w)) = 0
2((-24 + -3w) + w(-8 + -1w)) = 0
2(-24 + -3w + (-8 * w + -1w * w)) = 0
2(-24 + -3w + (-8w + -1w2)) = 0

Combine like terms: -3w + -8w = -11w
2(-24 + -11w + -1w2) = 0
(-24 * 2 + -11w * 2 + -1w2 * 2) = 0
(-48 + -22w + -2w2) = 0

Solving
-48 + -22w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(24 + 11w + w2) = 0

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

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

Simplifying
8 + w = 0

Solving
8 + w = 0

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

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

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

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

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

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Solution
w = {-8, -3}