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Simplifying (5w + -3)(7 + w) = 0 Reorder the terms: (-3 + 5w)(7 + w) = 0 Multiply (-3 + 5w) * (7 + w) (-3(7 + w) + 5w * (7 + w)) = 0 ((7 * -3 + w * -3) + 5w * (7 + w)) = 0 ((-21 + -3w) + 5w * (7 + w)) = 0 (-21 + -3w + (7 * 5w + w * 5w)) = 0 (-21 + -3w + (35w + 5w2)) = 0 Combine like terms: -3w + 35w = 32w (-21 + 32w + 5w2) = 0 Solving -21 + 32w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(3 + -5w) = 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 '(3 + -5w)' equal to zero and attempt to solve: Simplifying 3 + -5w = 0 Solving 3 + -5w = 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 + -5w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5w = 0 + -3 -5w = 0 + -3 Combine like terms: 0 + -3 = -3 -5w = -3 Divide each side by '-5'. w = 0.6 Simplifying w = 0.6Solution
w = {-7, 0.6}
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