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Simplifying (3w + -4)(4w + -6) = 0 Reorder the terms: (-4 + 3w)(4w + -6) = 0 Reorder the terms: (-4 + 3w)(-6 + 4w) = 0 Multiply (-4 + 3w) * (-6 + 4w) (-4(-6 + 4w) + 3w * (-6 + 4w)) = 0 ((-6 * -4 + 4w * -4) + 3w * (-6 + 4w)) = 0 ((24 + -16w) + 3w * (-6 + 4w)) = 0 (24 + -16w + (-6 * 3w + 4w * 3w)) = 0 (24 + -16w + (-18w + 12w2)) = 0 Combine like terms: -16w + -18w = -34w (24 + -34w + 12w2) = 0 Solving 24 + -34w + 12w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -17w + 6w2) = 0 Factor a trinomial. 2((4 + -3w)(3 + -2w)) = 0 Ignore the factor 2.Subproblem 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 '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {1.333333333, 1.5}
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