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Simplifying (1 + w)(3w + -8) = 0 Reorder the terms: (1 + w)(-8 + 3w) = 0 Multiply (1 + w) * (-8 + 3w) (1(-8 + 3w) + w(-8 + 3w)) = 0 ((-8 * 1 + 3w * 1) + w(-8 + 3w)) = 0 ((-8 + 3w) + w(-8 + 3w)) = 0 (-8 + 3w + (-8 * w + 3w * w)) = 0 (-8 + 3w + (-8w + 3w2)) = 0 Combine like terms: 3w + -8w = -5w (-8 + -5w + 3w2) = 0 Solving -8 + -5w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -1w)(8 + -3w) = 0Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
Set the factor '(8 + -3w)' equal to zero and attempt to solve: Simplifying 8 + -3w = 0 Solving 8 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3w = 0 + -8 -3w = 0 + -8 Combine like terms: 0 + -8 = -8 -3w = -8 Divide each side by '-3'. w = 2.666666667 Simplifying w = 2.666666667Solution
w = {-1, 2.666666667}
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