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Simplifying (6 + -1w)(3w + 5) = 0 Reorder the terms: (6 + -1w)(5 + 3w) = 0 Multiply (6 + -1w) * (5 + 3w) (6(5 + 3w) + -1w * (5 + 3w)) = 0 ((5 * 6 + 3w * 6) + -1w * (5 + 3w)) = 0 ((30 + 18w) + -1w * (5 + 3w)) = 0 (30 + 18w + (5 * -1w + 3w * -1w)) = 0 (30 + 18w + (-5w + -3w2)) = 0 Combine like terms: 18w + -5w = 13w (30 + 13w + -3w2) = 0 Solving 30 + 13w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (6 + -1w)(5 + 3w) = 0Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve: Simplifying 6 + -1w = 0 Solving 6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1w = 0 + -6 -1w = 0 + -6 Combine like terms: 0 + -6 = -6 -1w = -6 Divide each side by '-1'. w = 6 Simplifying w = 6Subproblem 2
Set the factor '(5 + 3w)' equal to zero and attempt to solve: Simplifying 5 + 3w = 0 Solving 5 + 3w = 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 + 3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3w = 0 + -5 3w = 0 + -5 Combine like terms: 0 + -5 = -5 3w = -5 Divide each side by '3'. w = -1.666666667 Simplifying w = -1.666666667Solution
w = {6, -1.666666667}
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