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Simplifying (3w + -7)(5 + -1w) = 0 Reorder the terms: (-7 + 3w)(5 + -1w) = 0 Multiply (-7 + 3w) * (5 + -1w) (-7(5 + -1w) + 3w * (5 + -1w)) = 0 ((5 * -7 + -1w * -7) + 3w * (5 + -1w)) = 0 ((-35 + 7w) + 3w * (5 + -1w)) = 0 (-35 + 7w + (5 * 3w + -1w * 3w)) = 0 (-35 + 7w + (15w + -3w2)) = 0 Combine like terms: 7w + 15w = 22w (-35 + 22w + -3w2) = 0 Solving -35 + 22w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + w)(7 + -3w) = 0Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5Subproblem 2
Set the factor '(7 + -3w)' equal to zero and attempt to solve: Simplifying 7 + -3w = 0 Solving 7 + -3w = 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 + -3w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3w = 0 + -7 -3w = 0 + -7 Combine like terms: 0 + -7 = -7 -3w = -7 Divide each side by '-3'. w = 2.333333333 Simplifying w = 2.333333333Solution
w = {5, 2.333333333}
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