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Simplifying (8w + 8)(4 + -1w) = 0 Reorder the terms: (8 + 8w)(4 + -1w) = 0 Multiply (8 + 8w) * (4 + -1w) (8(4 + -1w) + 8w * (4 + -1w)) = 0 ((4 * 8 + -1w * 8) + 8w * (4 + -1w)) = 0 ((32 + -8w) + 8w * (4 + -1w)) = 0 (32 + -8w + (4 * 8w + -1w * 8w)) = 0 (32 + -8w + (32w + -8w2)) = 0 Combine like terms: -8w + 32w = 24w (32 + 24w + -8w2) = 0 Solving 32 + 24w + -8w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '8'. 8(4 + 3w + -1w2) = 0 Factor a trinomial. 8((4 + -1w)(1 + w)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 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 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {4, -1}
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