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Simplifying 4w(3w + 4) = 3w + 4 Reorder the terms: 4w(4 + 3w) = 3w + 4 (4 * 4w + 3w * 4w) = 3w + 4 (16w + 12w2) = 3w + 4 Reorder the terms: 16w + 12w2 = 4 + 3w Solving 16w + 12w2 = 4 + 3w Solving for variable 'w'. Reorder the terms: -4 + 16w + -3w + 12w2 = 4 + 3w + -4 + -3w Combine like terms: 16w + -3w = 13w -4 + 13w + 12w2 = 4 + 3w + -4 + -3w Reorder the terms: -4 + 13w + 12w2 = 4 + -4 + 3w + -3w Combine like terms: 4 + -4 = 0 -4 + 13w + 12w2 = 0 + 3w + -3w -4 + 13w + 12w2 = 3w + -3w Combine like terms: 3w + -3w = 0 -4 + 13w + 12w2 = 0 Factor a trinomial. (-4 + -3w)(1 + -4w) = 0Subproblem 1
Set the factor '(-4 + -3w)' equal to zero and attempt to solve: Simplifying -4 + -3w = 0 Solving -4 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3w = 0 + 4 -3w = 0 + 4 Combine like terms: 0 + 4 = 4 -3w = 4 Divide each side by '-3'. w = -1.333333333 Simplifying w = -1.333333333Subproblem 2
Set the factor '(1 + -4w)' equal to zero and attempt to solve: Simplifying 1 + -4w = 0 Solving 1 + -4w = 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 + -4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4w = 0 + -1 -4w = 0 + -1 Combine like terms: 0 + -1 = -1 -4w = -1 Divide each side by '-4'. w = 0.25 Simplifying w = 0.25Solution
w = {-1.333333333, 0.25}
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