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Simplifying (3w + -1)(4w + 3) = 0 Reorder the terms: (-1 + 3w)(4w + 3) = 0 Reorder the terms: (-1 + 3w)(3 + 4w) = 0 Multiply (-1 + 3w) * (3 + 4w) (-1(3 + 4w) + 3w * (3 + 4w)) = 0 ((3 * -1 + 4w * -1) + 3w * (3 + 4w)) = 0 ((-3 + -4w) + 3w * (3 + 4w)) = 0 (-3 + -4w + (3 * 3w + 4w * 3w)) = 0 (-3 + -4w + (9w + 12w2)) = 0 Combine like terms: -4w + 9w = 5w (-3 + 5w + 12w2) = 0 Solving -3 + 5w + 12w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -4w)(1 + -3w) = 0Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve: Simplifying -3 + -4w = 0 Solving -3 + -4w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -4w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4w = 0 + 3 -4w = 0 + 3 Combine like terms: 0 + 3 = 3 -4w = 3 Divide each side by '-4'. w = -0.75 Simplifying w = -0.75Subproblem 2
Set the factor '(1 + -3w)' equal to zero and attempt to solve: Simplifying 1 + -3w = 0 Solving 1 + -3w = 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 + -3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3w = 0 + -1 -3w = 0 + -1 Combine like terms: 0 + -1 = -1 -3w = -1 Divide each side by '-3'. w = 0.3333333333 Simplifying w = 0.3333333333Solution
w = {-0.75, 0.3333333333}
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