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Simplifying (5w + -15)(15w + -5) = 0 Reorder the terms: (-15 + 5w)(15w + -5) = 0 Reorder the terms: (-15 + 5w)(-5 + 15w) = 0 Multiply (-15 + 5w) * (-5 + 15w) (-15(-5 + 15w) + 5w * (-5 + 15w)) = 0 ((-5 * -15 + 15w * -15) + 5w * (-5 + 15w)) = 0 ((75 + -225w) + 5w * (-5 + 15w)) = 0 (75 + -225w + (-5 * 5w + 15w * 5w)) = 0 (75 + -225w + (-25w + 75w2)) = 0 Combine like terms: -225w + -25w = -250w (75 + -250w + 75w2) = 0 Solving 75 + -250w + 75w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '25'. 25(3 + -10w + 3w2) = 0 Factor a trinomial. 25((1 + -3w)(3 + -1w)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(1 + -3w)' equal to zero and attempt to solve: Simplifying 1 + -3w = 0 Solving 1 + -3w = 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 + -3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3w = 0 + -1 -3w = 0 + -1 Combine like terms: 0 + -1 = -1 -3w = -1 Divide each side by '-3'. w = 0.3333333333 Simplifying w = 0.3333333333Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {0.3333333333, 3}
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