(2w+5)(6+w)=0

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Solution for (2w+5)(6+w)=0 equation:


Simplifying
(2w + 5)(6 + w) = 0

Reorder the terms:
(5 + 2w)(6 + w) = 0

Multiply (5 + 2w) * (6 + w)
(5(6 + w) + 2w * (6 + w)) = 0
((6 * 5 + w * 5) + 2w * (6 + w)) = 0
((30 + 5w) + 2w * (6 + w)) = 0
(30 + 5w + (6 * 2w + w * 2w)) = 0
(30 + 5w + (12w + 2w2)) = 0

Combine like terms: 5w + 12w = 17w
(30 + 17w + 2w2) = 0

Solving
30 + 17w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(5 + 2w) = 0

Subproblem 1

Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6

Subproblem 2

Set the factor '(5 + 2w)' equal to zero and attempt to solve: Simplifying 5 + 2w = 0 Solving 5 + 2w = 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 + 2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2w = 0 + -5 2w = 0 + -5 Combine like terms: 0 + -5 = -5 2w = -5 Divide each side by '2'. w = -2.5 Simplifying w = -2.5

Solution

w = {-6, -2.5}

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