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Simplifying (8 + w)(4w + -3) = 0 Reorder the terms: (8 + w)(-3 + 4w) = 0 Multiply (8 + w) * (-3 + 4w) (8(-3 + 4w) + w(-3 + 4w)) = 0 ((-3 * 8 + 4w * 8) + w(-3 + 4w)) = 0 ((-24 + 32w) + w(-3 + 4w)) = 0 (-24 + 32w + (-3 * w + 4w * w)) = 0 (-24 + 32w + (-3w + 4w2)) = 0 Combine like terms: 32w + -3w = 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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