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Simplifying (3w + -2)(4w + 4) = 0 Reorder the terms: (-2 + 3w)(4w + 4) = 0 Reorder the terms: (-2 + 3w)(4 + 4w) = 0 Multiply (-2 + 3w) * (4 + 4w) (-2(4 + 4w) + 3w * (4 + 4w)) = 0 ((4 * -2 + 4w * -2) + 3w * (4 + 4w)) = 0 ((-8 + -8w) + 3w * (4 + 4w)) = 0 (-8 + -8w + (4 * 3w + 4w * 3w)) = 0 (-8 + -8w + (12w + 12w2)) = 0 Combine like terms: -8w + 12w = 4w (-8 + 4w + 12w2) = 0 Solving -8 + 4w + 12w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + w + 3w2) = 0 Factor a trinomial. 4((-1 + -1w)(2 + -3w)) = 0 Ignore the factor 4.Subproblem 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 '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {-1, 0.6666666667}
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