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Simplifying (w + -3)(w + -3) = 2w2 + -10w + 12 Reorder the terms: (-3 + w)(w + -3) = 2w2 + -10w + 12 Reorder the terms: (-3 + w)(-3 + w) = 2w2 + -10w + 12 Multiply (-3 + w) * (-3 + w) (-3(-3 + w) + w(-3 + w)) = 2w2 + -10w + 12 ((-3 * -3 + w * -3) + w(-3 + w)) = 2w2 + -10w + 12 ((9 + -3w) + w(-3 + w)) = 2w2 + -10w + 12 (9 + -3w + (-3 * w + w * w)) = 2w2 + -10w + 12 (9 + -3w + (-3w + w2)) = 2w2 + -10w + 12 Combine like terms: -3w + -3w = -6w (9 + -6w + w2) = 2w2 + -10w + 12 Reorder the terms: 9 + -6w + w2 = 12 + -10w + 2w2 Solving 9 + -6w + w2 = 12 + -10w + 2w2 Solving for variable 'w'. Reorder the terms: 9 + -12 + -6w + 10w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2 Combine like terms: 9 + -12 = -3 -3 + -6w + 10w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2 Combine like terms: -6w + 10w = 4w -3 + 4w + w2 + -2w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2 Combine like terms: w2 + -2w2 = -1w2 -3 + 4w + -1w2 = 12 + -10w + 2w2 + -12 + 10w + -2w2 Reorder the terms: -3 + 4w + -1w2 = 12 + -12 + -10w + 10w + 2w2 + -2w2 Combine like terms: 12 + -12 = 0 -3 + 4w + -1w2 = 0 + -10w + 10w + 2w2 + -2w2 -3 + 4w + -1w2 = -10w + 10w + 2w2 + -2w2 Combine like terms: -10w + 10w = 0 -3 + 4w + -1w2 = 0 + 2w2 + -2w2 -3 + 4w + -1w2 = 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -3 + 4w + -1w2 = 0 Factor a trinomial. (-3 + w)(1 + -1w) = 0Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 w = 3 Simplifying w = 3Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {3, 1}
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