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Simplifying 10200 = (w + 3)(30) * w Reorder the terms: 10200 = (3 + w)(30) * w Reorder the terms for easier multiplication: 10200 = 30w(3 + w) 10200 = (3 * 30w + w * 30w) 10200 = (90w + 30w2) Solving 10200 = 90w + 30w2 Solving for variable 'w'. Reorder the terms: 10200 + -90w + -30w2 = 90w + -90w + 30w2 + -30w2 Combine like terms: 90w + -90w = 0 10200 + -90w + -30w2 = 0 + 30w2 + -30w2 10200 + -90w + -30w2 = 30w2 + -30w2 Combine like terms: 30w2 + -30w2 = 0 10200 + -90w + -30w2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(340 + -3w + -1w2) = 0 Factor a trinomial. 30((17 + -1w)(20 + w)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(17 + -1w)' equal to zero and attempt to solve: Simplifying 17 + -1w = 0 Solving 17 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -1w = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -1w = 0 + -17 -1w = 0 + -17 Combine like terms: 0 + -17 = -17 -1w = -17 Divide each side by '-1'. w = 17 Simplifying w = 17Subproblem 2
Set the factor '(20 + w)' equal to zero and attempt to solve: Simplifying 20 + w = 0 Solving 20 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + w = 0 + -20 Combine like terms: 20 + -20 = 0 0 + w = 0 + -20 w = 0 + -20 Combine like terms: 0 + -20 = -20 w = -20 Simplifying w = -20Solution
w = {17, -20}
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