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Simplifying 2w2 + 7w + 6 = w2 + 10w + 24 Reorder the terms: 6 + 7w + 2w2 = w2 + 10w + 24 Reorder the terms: 6 + 7w + 2w2 = 24 + 10w + w2 Solving 6 + 7w + 2w2 = 24 + 10w + w2 Solving for variable 'w'. Reorder the terms: 6 + -24 + 7w + -10w + 2w2 + -1w2 = 24 + 10w + w2 + -24 + -10w + -1w2 Combine like terms: 6 + -24 = -18 -18 + 7w + -10w + 2w2 + -1w2 = 24 + 10w + w2 + -24 + -10w + -1w2 Combine like terms: 7w + -10w = -3w -18 + -3w + 2w2 + -1w2 = 24 + 10w + w2 + -24 + -10w + -1w2 Combine like terms: 2w2 + -1w2 = 1w2 -18 + -3w + 1w2 = 24 + 10w + w2 + -24 + -10w + -1w2 Reorder the terms: -18 + -3w + 1w2 = 24 + -24 + 10w + -10w + w2 + -1w2 Combine like terms: 24 + -24 = 0 -18 + -3w + 1w2 = 0 + 10w + -10w + w2 + -1w2 -18 + -3w + 1w2 = 10w + -10w + w2 + -1w2 Combine like terms: 10w + -10w = 0 -18 + -3w + 1w2 = 0 + w2 + -1w2 -18 + -3w + 1w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -18 + -3w + 1w2 = 0 Factor a trinomial. (-3 + -1w)(6 + -1w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 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 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 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 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Solution
w = {-3, 6}
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