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Simplifying (3w + 8)(4 + w) = 0 Reorder the terms: (8 + 3w)(4 + w) = 0 Multiply (8 + 3w) * (4 + w) (8(4 + w) + 3w * (4 + w)) = 0 ((4 * 8 + w * 8) + 3w * (4 + w)) = 0 ((32 + 8w) + 3w * (4 + w)) = 0 (32 + 8w + (4 * 3w + w * 3w)) = 0 (32 + 8w + (12w + 3w2)) = 0 Combine like terms: 8w + 12w = 20w (32 + 20w + 3w2) = 0 Solving 32 + 20w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + w)(8 + 3w) = 0Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 2
Set the factor '(8 + 3w)' equal to zero and attempt to solve: Simplifying 8 + 3w = 0 Solving 8 + 3w = 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 + 3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3w = 0 + -8 3w = 0 + -8 Combine like terms: 0 + -8 = -8 3w = -8 Divide each side by '3'. w = -2.666666667 Simplifying w = -2.666666667Solution
w = {-4, -2.666666667}
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