(5w-8)(3+w)=0

Solution for (5w-8)(3+w)=0 equation:

Simplifying
(5w + -8)(3 + w) = 0

Reorder the terms:
(-8 + 5w)(3 + w) = 0

Multiply (-8 + 5w) * (3 + w)
(-8(3 + w) + 5w * (3 + w)) = 0
((3 * -8 + w * -8) + 5w * (3 + w)) = 0
((-24 + -8w) + 5w * (3 + w)) = 0
(-24 + -8w + (3 * 5w + w * 5w)) = 0
(-24 + -8w + (15w + 5w2)) = 0

Combine like terms: -8w + 15w = 7w
(-24 + 7w + 5w2) = 0

Solving
-24 + 7w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(8 + -5w) = 0

Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 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 + -1w = 0 + 3

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

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

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

Simplifying
w = -3
Subproblem 2
Set the factor '(8 + -5w)' equal to zero and attempt to solve:

Simplifying
8 + -5w = 0

Solving
8 + -5w = 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 + -5w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5w = 0 + -8
-5w = 0 + -8

Combine like terms: 0 + -8 = -8
-5w = -8

Divide each side by '-5'.
w = 1.6

Simplifying
w = 1.6
Solution
w = {-3, 1.6}