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Simplifying (7 + w)(5w + 3) = 0 Reorder the terms: (7 + w)(3 + 5w) = 0 Multiply (7 + w) * (3 + 5w) (7(3 + 5w) + w(3 + 5w)) = 0 ((3 * 7 + 5w * 7) + w(3 + 5w)) = 0 ((21 + 35w) + w(3 + 5w)) = 0 (21 + 35w + (3 * w + 5w * w)) = 0 (21 + 35w + (3w + 5w2)) = 0 Combine like terms: 35w + 3w = 38w (21 + 38w + 5w2) = 0 Solving 21 + 38w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + w)(3 + 5w) = 0Subproblem 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 '(3 + 5w)' equal to zero and attempt to solve: Simplifying 3 + 5w = 0 Solving 3 + 5w = 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 + 5w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5w = 0 + -3 5w = 0 + -3 Combine like terms: 0 + -3 = -3 5w = -3 Divide each side by '5'. w = -0.6 Simplifying w = -0.6Solution
w = {-7, -0.6}
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