(9-w)(4w-1)=0

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Solution for (9-w)(4w-1)=0 equation:


Simplifying
(9 + -1w)(4w + -1) = 0

Reorder the terms:
(9 + -1w)(-1 + 4w) = 0

Multiply (9 + -1w) * (-1 + 4w)
(9(-1 + 4w) + -1w * (-1 + 4w)) = 0
((-1 * 9 + 4w * 9) + -1w * (-1 + 4w)) = 0
((-9 + 36w) + -1w * (-1 + 4w)) = 0
(-9 + 36w + (-1 * -1w + 4w * -1w)) = 0
(-9 + 36w + (1w + -4w2)) = 0

Combine like terms: 36w + 1w = 37w
(-9 + 37w + -4w2) = 0

Solving
-9 + 37w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + w)(1 + -4w) = 0

Subproblem 1

Set the factor '(-9 + w)' equal to zero and attempt to solve: Simplifying -9 + w = 0 Solving -9 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w = 0 + 9 w = 0 + 9 Combine like terms: 0 + 9 = 9 w = 9 Simplifying w = 9

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 = {9, 0.25}

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