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Simplifying (5w + 5)(w + 7) = 0 Reorder the terms: (5 + 5w)(w + 7) = 0 Reorder the terms: (5 + 5w)(7 + w) = 0 Multiply (5 + 5w) * (7 + w) (5(7 + w) + 5w * (7 + w)) = 0 ((7 * 5 + w * 5) + 5w * (7 + w)) = 0 ((35 + 5w) + 5w * (7 + w)) = 0 (35 + 5w + (7 * 5w + w * 5w)) = 0 (35 + 5w + (35w + 5w2)) = 0 Combine like terms: 5w + 35w = 40w (35 + 40w + 5w2) = 0 Solving 35 + 40w + 5w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '5'. 5(7 + 8w + w2) = 0 Factor a trinomial. 5((7 + w)(1 + w)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {-7, -1}
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