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Simplifying (8w + 3)(5w + -15) = 0 Reorder the terms: (3 + 8w)(5w + -15) = 0 Reorder the terms: (3 + 8w)(-15 + 5w) = 0 Multiply (3 + 8w) * (-15 + 5w) (3(-15 + 5w) + 8w * (-15 + 5w)) = 0 ((-15 * 3 + 5w * 3) + 8w * (-15 + 5w)) = 0 ((-45 + 15w) + 8w * (-15 + 5w)) = 0 (-45 + 15w + (-15 * 8w + 5w * 8w)) = 0 (-45 + 15w + (-120w + 40w2)) = 0 Combine like terms: 15w + -120w = -105w (-45 + -105w + 40w2) = 0 Solving -45 + -105w + 40w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -21w + 8w2) = 0 Factor a trinomial. 5((-3 + -8w)(3 + -1w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -8w)' equal to zero and attempt to solve: Simplifying -3 + -8w = 0 Solving -3 + -8w = 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 + -8w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8w = 0 + 3 -8w = 0 + 3 Combine like terms: 0 + 3 = 3 -8w = 3 Divide each side by '-8'. w = -0.375 Simplifying w = -0.375Subproblem 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 = {-0.375, 3}
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