(2w+9)(5+w)=0

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Solution for (2w+9)(5+w)=0 equation:


Simplifying
(2w + 9)(5 + w) = 0

Reorder the terms:
(9 + 2w)(5 + w) = 0

Multiply (9 + 2w) * (5 + w)
(9(5 + w) + 2w * (5 + w)) = 0
((5 * 9 + w * 9) + 2w * (5 + w)) = 0
((45 + 9w) + 2w * (5 + w)) = 0
(45 + 9w + (5 * 2w + w * 2w)) = 0
(45 + 9w + (10w + 2w2)) = 0

Combine like terms: 9w + 10w = 19w
(45 + 19w + 2w2) = 0

Solving
45 + 19w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + w)(9 + 2w) = 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 '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 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 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5

Solution

w = {-5, -4.5}

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