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Simplifying (3w + -15)(15w + -3) = 0 Reorder the terms: (-15 + 3w)(15w + -3) = 0 Reorder the terms: (-15 + 3w)(-3 + 15w) = 0 Multiply (-15 + 3w) * (-3 + 15w) (-15(-3 + 15w) + 3w * (-3 + 15w)) = 0 ((-3 * -15 + 15w * -15) + 3w * (-3 + 15w)) = 0 ((45 + -225w) + 3w * (-3 + 15w)) = 0 (45 + -225w + (-3 * 3w + 15w * 3w)) = 0 (45 + -225w + (-9w + 45w2)) = 0 Combine like terms: -225w + -9w = -234w (45 + -234w + 45w2) = 0 Solving 45 + -234w + 45w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '9'. 9(5 + -26w + 5w2) = 0 Factor a trinomial. 9((1 + -5w)(5 + -1w)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(1 + -5w)' equal to zero and attempt to solve: Simplifying 1 + -5w = 0 Solving 1 + -5w = 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 + -5w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5w = 0 + -1 -5w = 0 + -1 Combine like terms: 0 + -1 = -1 -5w = -1 Divide each side by '-5'. w = 0.2 Simplifying w = 0.2Subproblem 2
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 = 5Solution
w = {0.2, 5}
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