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Simplifying (5w + 1)(6 + w) = 0 Reorder the terms: (1 + 5w)(6 + w) = 0 Multiply (1 + 5w) * (6 + w) (1(6 + w) + 5w * (6 + w)) = 0 ((6 * 1 + w * 1) + 5w * (6 + w)) = 0 ((6 + 1w) + 5w * (6 + w)) = 0 (6 + 1w + (6 * 5w + w * 5w)) = 0 (6 + 1w + (30w + 5w2)) = 0 Combine like terms: 1w + 30w = 31w (6 + 31w + 5w2) = 0 Solving 6 + 31w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (6 + w)(1 + 5w) = 0Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Subproblem 2
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 = -0.2Solution
w = {-6, -0.2}
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