(8+w)(4w-1)=0

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Solution for (8+w)(4w-1)=0 equation:


Simplifying
(8 + w)(4w + -1) = 0

Reorder the terms:
(8 + w)(-1 + 4w) = 0

Multiply (8 + w) * (-1 + 4w)
(8(-1 + 4w) + w(-1 + 4w)) = 0
((-1 * 8 + 4w * 8) + w(-1 + 4w)) = 0
((-8 + 32w) + w(-1 + 4w)) = 0
(-8 + 32w + (-1 * w + 4w * w)) = 0
(-8 + 32w + (-1w + 4w2)) = 0

Combine like terms: 32w + -1w = 31w
(-8 + 31w + 4w2) = 0

Solving
-8 + 31w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + -1w)(1 + -4w) = 0

Subproblem 1

Set the factor '(-8 + -1w)' equal to zero and attempt to solve: Simplifying -8 + -1w = 0 Solving -8 + -1w = 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 + -1w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1w = 0 + 8 -1w = 0 + 8 Combine like terms: 0 + 8 = 8 -1w = 8 Divide each side by '-1'. w = -8 Simplifying w = -8

Subproblem 2

Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25

Solution

w = {-8, 0.25}

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