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Simplifying (3w + 4)(w + 3) = 22 Reorder the terms: (4 + 3w)(w + 3) = 22 Reorder the terms: (4 + 3w)(3 + w) = 22 Multiply (4 + 3w) * (3 + w) (4(3 + w) + 3w * (3 + w)) = 22 ((3 * 4 + w * 4) + 3w * (3 + w)) = 22 ((12 + 4w) + 3w * (3 + w)) = 22 (12 + 4w + (3 * 3w + w * 3w)) = 22 (12 + 4w + (9w + 3w2)) = 22 Combine like terms: 4w + 9w = 13w (12 + 13w + 3w2) = 22 Solving 12 + 13w + 3w2 = 22 Solving for variable 'w'. Reorder the terms: 12 + -22 + 13w + 3w2 = 22 + -22 Combine like terms: 12 + -22 = -10 -10 + 13w + 3w2 = 22 + -22 Combine like terms: 22 + -22 = 0 -10 + 13w + 3w2 = 0 Factor a trinomial. (-5 + -1w)(2 + -3w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 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 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {-5, 0.6666666667}
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