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Simplifying (2w + -5)(3 + -1w) = 0 Reorder the terms: (-5 + 2w)(3 + -1w) = 0 Multiply (-5 + 2w) * (3 + -1w) (-5(3 + -1w) + 2w * (3 + -1w)) = 0 ((3 * -5 + -1w * -5) + 2w * (3 + -1w)) = 0 ((-15 + 5w) + 2w * (3 + -1w)) = 0 (-15 + 5w + (3 * 2w + -1w * 2w)) = 0 (-15 + 5w + (6w + -2w2)) = 0 Combine like terms: 5w + 6w = 11w (-15 + 11w + -2w2) = 0 Solving -15 + 11w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + w)(5 + -2w) = 0Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 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 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 w = 3 Simplifying w = 3Subproblem 2
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 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 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {3, 2.5}
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