(2w+3)(8+w)=0

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Solution for (2w+3)(8+w)=0 equation:


Simplifying
(2w + 3)(8 + w) = 0

Reorder the terms:
(3 + 2w)(8 + w) = 0

Multiply (3 + 2w) * (8 + w)
(3(8 + w) + 2w * (8 + w)) = 0
((8 * 3 + w * 3) + 2w * (8 + w)) = 0
((24 + 3w) + 2w * (8 + w)) = 0
(24 + 3w + (8 * 2w + w * 2w)) = 0
(24 + 3w + (16w + 2w2)) = 0

Combine like terms: 3w + 16w = 19w
(24 + 19w + 2w2) = 0

Solving
24 + 19w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(8 + w)(3 + 2w) = 0

Subproblem 1

Set the factor '(8 + w)' equal to zero and attempt to solve: Simplifying 8 + w = 0 Solving 8 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + w = 0 + -8 w = 0 + -8 Combine like terms: 0 + -8 = -8 w = -8 Simplifying w = -8

Subproblem 2

Set the factor '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5

Solution

w = {-8, -1.5}

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