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

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


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

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

Multiply (4 + -1w) * (5 + 4w)
(4(5 + 4w) + -1w * (5 + 4w)) = 0
((5 * 4 + 4w * 4) + -1w * (5 + 4w)) = 0
((20 + 16w) + -1w * (5 + 4w)) = 0
(20 + 16w + (5 * -1w + 4w * -1w)) = 0
(20 + 16w + (-5w + -4w2)) = 0

Combine like terms: 16w + -5w = 11w
(20 + 11w + -4w2) = 0

Solving
20 + 11w + -4w2 = 0

Solving for variable 'w'.

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

Subproblem 1

Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4

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 = {4, -1.25}

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