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Simplifying (4w + -3)(8 + w) = 0 Reorder the terms: (-3 + 4w)(8 + w) = 0 Multiply (-3 + 4w) * (8 + w) (-3(8 + w) + 4w * (8 + w)) = 0 ((8 * -3 + w * -3) + 4w * (8 + w)) = 0 ((-24 + -3w) + 4w * (8 + w)) = 0 (-24 + -3w + (8 * 4w + w * 4w)) = 0 (-24 + -3w + (32w + 4w2)) = 0 Combine like terms: -3w + 32w = 29w (-24 + 29w + 4w2) = 0 Solving -24 + 29w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-8 + -1w)(3 + -4w) = 0Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve: Simplifying -8 + -1w = 0 Solving -8 + -1w = 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 + -1w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1w = 0 + 8 -1w = 0 + 8 Combine like terms: 0 + 8 = 8 -1w = 8 Divide each side by '-1'. w = -8 Simplifying w = -8Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve: Simplifying 3 + -4w = 0 Solving 3 + -4w = 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 + -4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4w = 0 + -3 -4w = 0 + -3 Combine like terms: 0 + -3 = -3 -4w = -3 Divide each side by '-4'. w = 0.75 Simplifying w = 0.75Solution
w = {-8, 0.75}
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