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Simplifying (w + -6)(2w + -7) = 0 Reorder the terms: (-6 + w)(2w + -7) = 0 Reorder the terms: (-6 + w)(-7 + 2w) = 0 Multiply (-6 + w) * (-7 + 2w) (-6(-7 + 2w) + w(-7 + 2w)) = 0 ((-7 * -6 + 2w * -6) + w(-7 + 2w)) = 0 ((42 + -12w) + w(-7 + 2w)) = 0 (42 + -12w + (-7 * w + 2w * w)) = 0 (42 + -12w + (-7w + 2w2)) = 0 Combine like terms: -12w + -7w = -19w (42 + -19w + 2w2) = 0 Solving 42 + -19w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + -2w)(6 + -1w) = 0Subproblem 1
Set the factor '(7 + -2w)' equal to zero and attempt to solve: Simplifying 7 + -2w = 0 Solving 7 + -2w = 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 + -2w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2w = 0 + -7 -2w = 0 + -7 Combine like terms: 0 + -7 = -7 -2w = -7 Divide each side by '-2'. w = 3.5 Simplifying w = 3.5Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 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 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {3.5, 6}
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