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Simplifying (w + 3)(w + 3) = 2w2 + 10w + -3 Reorder the terms: (3 + w)(w + 3) = 2w2 + 10w + -3 Reorder the terms: (3 + w)(3 + w) = 2w2 + 10w + -3 Multiply (3 + w) * (3 + w) (3(3 + w) + w(3 + w)) = 2w2 + 10w + -3 ((3 * 3 + w * 3) + w(3 + w)) = 2w2 + 10w + -3 ((9 + 3w) + w(3 + w)) = 2w2 + 10w + -3 (9 + 3w + (3 * w + w * w)) = 2w2 + 10w + -3 (9 + 3w + (3w + w2)) = 2w2 + 10w + -3 Combine like terms: 3w + 3w = 6w (9 + 6w + w2) = 2w2 + 10w + -3 Reorder the terms: 9 + 6w + w2 = -3 + 10w + 2w2 Solving 9 + 6w + w2 = -3 + 10w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + 3 + 6w + -10w + w2 + -2w2 = -3 + 10w + 2w2 + 3 + -10w + -2w2 Combine like terms: 9 + 3 = 12 12 + 6w + -10w + w2 + -2w2 = -3 + 10w + 2w2 + 3 + -10w + -2w2 Combine like terms: 6w + -10w = -4w 12 + -4w + w2 + -2w2 = -3 + 10w + 2w2 + 3 + -10w + -2w2 Combine like terms: w2 + -2w2 = -1w2 12 + -4w + -1w2 = -3 + 10w + 2w2 + 3 + -10w + -2w2 Reorder the terms: 12 + -4w + -1w2 = -3 + 3 + 10w + -10w + 2w2 + -2w2 Combine like terms: -3 + 3 = 0 12 + -4w + -1w2 = 0 + 10w + -10w + 2w2 + -2w2 12 + -4w + -1w2 = 10w + -10w + 2w2 + -2w2 Combine like terms: 10w + -10w = 0 12 + -4w + -1w2 = 0 + 2w2 + -2w2 12 + -4w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 12 + -4w + -1w2 = 0 Factor a trinomial. (2 + -1w)(6 + w) = 0Subproblem 1
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 = 2Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve: Simplifying 6 + w = 0 Solving 6 + w = 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 + w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + w = 0 + -6 w = 0 + -6 Combine like terms: 0 + -6 = -6 w = -6 Simplifying w = -6Solution
w = {2, -6}
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