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Simplifying (3w + -8)(2w + 1) = 0 Reorder the terms: (-8 + 3w)(2w + 1) = 0 Reorder the terms: (-8 + 3w)(1 + 2w) = 0 Multiply (-8 + 3w) * (1 + 2w) (-8(1 + 2w) + 3w * (1 + 2w)) = 0 ((1 * -8 + 2w * -8) + 3w * (1 + 2w)) = 0 ((-8 + -16w) + 3w * (1 + 2w)) = 0 (-8 + -16w + (1 * 3w + 2w * 3w)) = 0 (-8 + -16w + (3w + 6w2)) = 0 Combine like terms: -16w + 3w = -13w (-8 + -13w + 6w2) = 0 Solving -8 + -13w + 6w2 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -2w)(8 + -3w) = 0Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve: Simplifying -1 + -2w = 0 Solving -1 + -2w = 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 + -2w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2w = 0 + 1 -2w = 0 + 1 Combine like terms: 0 + 1 = 1 -2w = 1 Divide each side by '-2'. w = -0.5 Simplifying w = -0.5Subproblem 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 = {-0.5, 2.666666667}
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