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

Solution for (3w-8)(1+w)=0 equation:

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

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

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

Combine like terms: -8w + 3w = -5w
(-8 + -5w + 3w2) = 0

Solving
-8 + -5w + 3w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

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

Simplifying
8 + -3w = 0

Solving
8 + -3w = 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 + -3w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3w = 0 + -8
-3w = 0 + -8

Combine like terms: 0 + -8 = -8
-3w = -8

Divide each side by '-3'.
w = 2.666666667

Simplifying
w = 2.666666667
Solution
w = {-1, 2.666666667}