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Simplifying (9 + w)(3w + 2) = 0 Reorder the terms: (9 + w)(2 + 3w) = 0 Multiply (9 + w) * (2 + 3w) (9(2 + 3w) + w(2 + 3w)) = 0 ((2 * 9 + 3w * 9) + w(2 + 3w)) = 0 ((18 + 27w) + w(2 + 3w)) = 0 (18 + 27w + (2 * w + 3w * w)) = 0 (18 + 27w + (2w + 3w2)) = 0 Combine like terms: 27w + 2w = 29w (18 + 29w + 3w2) = 0 Solving 18 + 29w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + w)(2 + 3w) = 0Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve: Simplifying 9 + w = 0 Solving 9 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w = 0 + -9 w = 0 + -9 Combine like terms: 0 + -9 = -9 w = -9 Simplifying w = -9Subproblem 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 = {-9, -0.6666666667}
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