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Simplifying (3w + 1)(w) = 14 Reorder the terms: (1 + 3w)(w) = 14 Reorder the terms for easier multiplication: w(1 + 3w) = 14 (1 * w + 3w * w) = 14 (1w + 3w2) = 14 Solving 1w + 3w2 = 14 Solving for variable 'w'. Reorder the terms: -14 + 1w + 3w2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 1w + 3w2 = 0 Factor a trinomial. (-7 + -3w)(2 + -1w) = 0Subproblem 1
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 = -2.333333333Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Solution
w = {-2.333333333, 2}
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