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

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


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

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

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

Combine like terms: 3w + 8w = 11w
(-8 + 11w + -3w2) = 0

Solving
-8 + 11w + -3w2 = 0

Solving for variable 'w'.

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


Subproblem 1
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

Subproblem 2
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
Solution
w = {2.666666667, 1}

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