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

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Solution for (1+w)(4w-5)=0 equation:


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

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

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

Combine like terms: 4w + -5w = -1w
(-5 + -1w + 4w2) = 0

Solving
-5 + -1w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(5 + -4w) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(5 + -4w)' equal to zero and attempt to solve: Simplifying 5 + -4w = 0 Solving 5 + -4w = 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 + -4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4w = 0 + -5 -4w = 0 + -5 Combine like terms: 0 + -5 = -5 -4w = -5 Divide each side by '-4'. w = 1.25 Simplifying w = 1.25

Solution

w = {-1, 1.25}

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