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Simplifying (4w + 6)(4w + 6) = 0 Reorder the terms: (6 + 4w)(4w + 6) = 0 Reorder the terms: (6 + 4w)(6 + 4w) = 0 Multiply (6 + 4w) * (6 + 4w) (6(6 + 4w) + 4w * (6 + 4w)) = 0 ((6 * 6 + 4w * 6) + 4w * (6 + 4w)) = 0 ((36 + 24w) + 4w * (6 + 4w)) = 0 (36 + 24w + (6 * 4w + 4w * 4w)) = 0 (36 + 24w + (24w + 16w2)) = 0 Combine like terms: 24w + 24w = 48w (36 + 48w + 16w2) = 0 Solving 36 + 48w + 16w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + 12w + 4w2) = 0 Factor a trinomial. 4((3 + 2w)(3 + 2w)) = 0 Ignore the factor 4.Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, -1.5}
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