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Simplifying (7 + w)(3w + 1) = 0 Reorder the terms: (7 + w)(1 + 3w) = 0 Multiply (7 + w) * (1 + 3w) (7(1 + 3w) + w(1 + 3w)) = 0 ((1 * 7 + 3w * 7) + w(1 + 3w)) = 0 ((7 + 21w) + w(1 + 3w)) = 0 (7 + 21w + (1 * w + 3w * w)) = 0 (7 + 21w + (1w + 3w2)) = 0 Combine like terms: 21w + 1w = 22w (7 + 22w + 3w2) = 0 Solving 7 + 22w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + w)(1 + 3w) = 0Subproblem 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 '(1 + 3w)' equal to zero and attempt to solve: Simplifying 1 + 3w = 0 Solving 1 + 3w = 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 + 3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3w = 0 + -1 3w = 0 + -1 Combine like terms: 0 + -1 = -1 3w = -1 Divide each side by '3'. w = -0.3333333333 Simplifying w = -0.3333333333Solution
w = {-7, -0.3333333333}
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