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