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Simplifying (5w + 6)(7 + -1w) = 0 Reorder the terms: (6 + 5w)(7 + -1w) = 0 Multiply (6 + 5w) * (7 + -1w) (6(7 + -1w) + 5w * (7 + -1w)) = 0 ((7 * 6 + -1w * 6) + 5w * (7 + -1w)) = 0 ((42 + -6w) + 5w * (7 + -1w)) = 0 (42 + -6w + (7 * 5w + -1w * 5w)) = 0 (42 + -6w + (35w + -5w2)) = 0 Combine like terms: -6w + 35w = 29w (42 + 29w + -5w2) = 0 Solving 42 + 29w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + -1w)(6 + 5w) = 0Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Subproblem 2
Set the factor '(6 + 5w)' equal to zero and attempt to solve: Simplifying 6 + 5w = 0 Solving 6 + 5w = 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 + 5w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5w = 0 + -6 5w = 0 + -6 Combine like terms: 0 + -6 = -6 5w = -6 Divide each side by '5'. w = -1.2 Simplifying w = -1.2Solution
w = {7, -1.2}
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