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

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


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

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

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

Combine like terms: 1w + 24w = 25w
(-8 + 25w + -3w2) = 0

Solving
-8 + 25w + -3w2 = 0

Solving for variable 'w'.

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

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 '(1 + -3w)' equal to zero and attempt to solve: Simplifying 1 + -3w = 0 Solving 1 + -3w = 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 + -3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3w = 0 + -1 -3w = 0 + -1 Combine like terms: 0 + -1 = -1 -3w = -1 Divide each side by '-3'. w = 0.3333333333 Simplifying w = 0.3333333333

Solution

w = {8, 0.3333333333}

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