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Simplifying (7 + w)(4w + 6) = 0 Reorder the terms: (7 + w)(6 + 4w) = 0 Multiply (7 + w) * (6 + 4w) (7(6 + 4w) + w(6 + 4w)) = 0 ((6 * 7 + 4w * 7) + w(6 + 4w)) = 0 ((42 + 28w) + w(6 + 4w)) = 0 (42 + 28w + (6 * w + 4w * w)) = 0 (42 + 28w + (6w + 4w2)) = 0 Combine like terms: 28w + 6w = 34w (42 + 34w + 4w2) = 0 Solving 42 + 34w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 17w + 2w2) = 0 Factor a trinomial. 2((7 + w)(3 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Subproblem 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 = {-7, -1.5}
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