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Simplifying (3w + 7)(8 + -1w) = 0 Reorder the terms: (7 + 3w)(8 + -1w) = 0 Multiply (7 + 3w) * (8 + -1w) (7(8 + -1w) + 3w * (8 + -1w)) = 0 ((8 * 7 + -1w * 7) + 3w * (8 + -1w)) = 0 ((56 + -7w) + 3w * (8 + -1w)) = 0 (56 + -7w + (8 * 3w + -1w * 3w)) = 0 (56 + -7w + (24w + -3w2)) = 0 Combine like terms: -7w + 24w = 17w (56 + 17w + -3w2) = 0 Solving 56 + 17w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (8 + -1w)(7 + 3w) = 0Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. w = 8 Simplifying w = 8Subproblem 2
Set the factor '(7 + 3w)' equal to zero and attempt to solve: Simplifying 7 + 3w = 0 Solving 7 + 3w = 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 + 3w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3w = 0 + -7 3w = 0 + -7 Combine like terms: 0 + -7 = -7 3w = -7 Divide each side by '3'. w = -2.333333333 Simplifying w = -2.333333333Solution
w = {8, -2.333333333}
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