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

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


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

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

Multiply (7 + w) * (5 + 4w)
(7(5 + 4w) + w(5 + 4w)) = 0
((5 * 7 + 4w * 7) + w(5 + 4w)) = 0
((35 + 28w) + w(5 + 4w)) = 0
(35 + 28w + (5 * w + 4w * w)) = 0
(35 + 28w + (5w + 4w2)) = 0

Combine like terms: 28w + 5w = 33w
(35 + 33w + 4w2) = 0

Solving
35 + 33w + 4w2 = 0

Solving for variable 'w'.

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

Subproblem 1

Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7

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 = {-7, -1.25}

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