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Simplifying (8 + -1w)(4w + -6) = 0 Reorder the terms: (8 + -1w)(-6 + 4w) = 0 Multiply (8 + -1w) * (-6 + 4w) (8(-6 + 4w) + -1w * (-6 + 4w)) = 0 ((-6 * 8 + 4w * 8) + -1w * (-6 + 4w)) = 0 ((-48 + 32w) + -1w * (-6 + 4w)) = 0 (-48 + 32w + (-6 * -1w + 4w * -1w)) = 0 (-48 + 32w + (6w + -4w2)) = 0 Combine like terms: 32w + 6w = 38w (-48 + 38w + -4w2) = 0 Solving -48 + 38w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 19w + -2w2) = 0 Factor a trinomial. 2((-8 + w)(3 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + w)' equal to zero and attempt to solve: Simplifying -8 + w = 0 Solving -8 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + w = 0 + 8 w = 0 + 8 Combine like terms: 0 + 8 = 8 w = 8 Simplifying w = 8Subproblem 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 = {8, 1.5}
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