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Simplifying (3w + 10)(-2w + 5) = 0 Reorder the terms: (10 + 3w)(-2w + 5) = 0 Reorder the terms: (10 + 3w)(5 + -2w) = 0 Multiply (10 + 3w) * (5 + -2w) (10(5 + -2w) + 3w * (5 + -2w)) = 0 ((5 * 10 + -2w * 10) + 3w * (5 + -2w)) = 0 ((50 + -20w) + 3w * (5 + -2w)) = 0 (50 + -20w + (5 * 3w + -2w * 3w)) = 0 (50 + -20w + (15w + -6w2)) = 0 Combine like terms: -20w + 15w = -5w (50 + -5w + -6w2) = 0 Solving 50 + -5w + -6w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + -2w)(10 + 3w) = 0Subproblem 1
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 = 2.5Subproblem 2
Set the factor '(10 + 3w)' equal to zero and attempt to solve: Simplifying 10 + 3w = 0 Solving 10 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 3w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3w = 0 + -10 3w = 0 + -10 Combine like terms: 0 + -10 = -10 3w = -10 Divide each side by '3'. w = -3.333333333 Simplifying w = -3.333333333Solution
w = {2.5, -3.333333333}
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