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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 = 23w (-30 + 23w + -3w2) = 0 Solving -30 + 23w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-6 + w)(5 + -3w) = 0Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve: Simplifying -6 + w = 0 Solving -6 + w = 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 + w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + w = 0 + 6 w = 0 + 6 Combine like terms: 0 + 6 = 6 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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