(3w-8)(6-w)=0

Solution for (3w-8)(6-w)=0 equation:

Simplifying
(3w + -8)(6 + -1w) = 0

Reorder the terms:
(-8 + 3w)(6 + -1w) = 0

Multiply (-8 + 3w) * (6 + -1w)
(-8(6 + -1w) + 3w * (6 + -1w)) = 0
((6 * -8 + -1w * -8) + 3w * (6 + -1w)) = 0
((-48 + 8w) + 3w * (6 + -1w)) = 0
(-48 + 8w + (6 * 3w + -1w * 3w)) = 0
(-48 + 8w + (18w + -3w2)) = 0

Combine like terms: 8w + 18w = 26w
(-48 + 26w + -3w2) = 0

Solving
-48 + 26w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + w)(8 + -3w) = 0

Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve:

Simplifying
-6 + w = 0

Solving
-6 + w = 0

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

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

Combine like terms: -6 + 6 = 0
0 + w = 0 + 6
w = 0 + 6

Combine like terms: 0 + 6 = 6
w = 6

Simplifying
w = 6
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 = {6, 2.666666667}