(5-w)(4w-7)=0

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Solution for (5-w)(4w-7)=0 equation:


Simplifying
(5 + -1w)(4w + -7) = 0

Reorder the terms:
(5 + -1w)(-7 + 4w) = 0

Multiply (5 + -1w) * (-7 + 4w)
(5(-7 + 4w) + -1w * (-7 + 4w)) = 0
((-7 * 5 + 4w * 5) + -1w * (-7 + 4w)) = 0
((-35 + 20w) + -1w * (-7 + 4w)) = 0
(-35 + 20w + (-7 * -1w + 4w * -1w)) = 0
(-35 + 20w + (7w + -4w2)) = 0

Combine like terms: 20w + 7w = 27w
(-35 + 27w + -4w2) = 0

Solving
-35 + 27w + -4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + w)(7 + -4w) = 0

Subproblem 1

Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5

Subproblem 2

Set the factor '(7 + -4w)' equal to zero and attempt to solve: Simplifying 7 + -4w = 0 Solving 7 + -4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4w = 0 + -7 -4w = 0 + -7 Combine like terms: 0 + -7 = -7 -4w = -7 Divide each side by '-4'. w = 1.75 Simplifying w = 1.75

Solution

w = {5, 1.75}

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