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Simplifying (4w + -3)(5w + 5) = 0 Reorder the terms: (-3 + 4w)(5w + 5) = 0 Reorder the terms: (-3 + 4w)(5 + 5w) = 0 Multiply (-3 + 4w) * (5 + 5w) (-3(5 + 5w) + 4w * (5 + 5w)) = 0 ((5 * -3 + 5w * -3) + 4w * (5 + 5w)) = 0 ((-15 + -15w) + 4w * (5 + 5w)) = 0 (-15 + -15w + (5 * 4w + 5w * 4w)) = 0 (-15 + -15w + (20w + 20w2)) = 0 Combine like terms: -15w + 20w = 5w (-15 + 5w + 20w2) = 0 Solving -15 + 5w + 20w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + w + 4w2) = 0 Factor a trinomial. 5((-1 + -1w)(3 + -4w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 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 = {-1, 0.75}
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