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Simplifying (2w + 7)(w + -6) = 0 Reorder the terms: (7 + 2w)(w + -6) = 0 Reorder the terms: (7 + 2w)(-6 + w) = 0 Multiply (7 + 2w) * (-6 + w) (7(-6 + w) + 2w * (-6 + w)) = 0 ((-6 * 7 + w * 7) + 2w * (-6 + w)) = 0 ((-42 + 7w) + 2w * (-6 + w)) = 0 (-42 + 7w + (-6 * 2w + w * 2w)) = 0 (-42 + 7w + (-12w + 2w2)) = 0 Combine like terms: 7w + -12w = -5w (-42 + -5w + 2w2) = 0 Solving -42 + -5w + 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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