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Simplifying (w + 7)(w + -2) = 0 Reorder the terms: (7 + w)(w + -2) = 0 Reorder the terms: (7 + w)(-2 + w) = 0 Multiply (7 + w) * (-2 + w) (7(-2 + w) + w(-2 + w)) = 0 ((-2 * 7 + w * 7) + w(-2 + w)) = 0 ((-14 + 7w) + w(-2 + w)) = 0 (-14 + 7w + (-2 * w + w * w)) = 0 (-14 + 7w + (-2w + w2)) = 0 Combine like terms: 7w + -2w = 5w (-14 + 5w + w2) = 0 Solving -14 + 5w + w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(2 + -1w) = 0Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 2
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 = 2Solution
w = {-7, 2}
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