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Simplifying (4w + -3)(5 + w) = 0 Reorder the terms: (-3 + 4w)(5 + w) = 0 Multiply (-3 + 4w) * (5 + w) (-3(5 + w) + 4w * (5 + w)) = 0 ((5 * -3 + w * -3) + 4w * (5 + w)) = 0 ((-15 + -3w) + 4w * (5 + w)) = 0 (-15 + -3w + (5 * 4w + w * 4w)) = 0 (-15 + -3w + (20w + 4w2)) = 0 Combine like terms: -3w + 20w = 17w (-15 + 17w + 4w2) = 0 Solving -15 + 17w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(3 + -4w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 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 = {-5, 0.75}
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