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Simplifying (6 + -1w)(4w + -2) = 0 Reorder the terms: (6 + -1w)(-2 + 4w) = 0 Multiply (6 + -1w) * (-2 + 4w) (6(-2 + 4w) + -1w * (-2 + 4w)) = 0 ((-2 * 6 + 4w * 6) + -1w * (-2 + 4w)) = 0 ((-12 + 24w) + -1w * (-2 + 4w)) = 0 (-12 + 24w + (-2 * -1w + 4w * -1w)) = 0 (-12 + 24w + (2w + -4w2)) = 0 Combine like terms: 24w + 2w = 26w (-12 + 26w + -4w2) = 0 Solving -12 + 26w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 13w + -2w2) = 0 Factor a trinomial. 2((-6 + w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + w)' equal to zero and attempt to solve: Simplifying -6 + w = 0 Solving -6 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + w = 0 + 6 w = 0 + 6 Combine like terms: 0 + 6 = 6 w = 6 Simplifying w = 6Subproblem 2
Set the factor '(1 + -2w)' equal to zero and attempt to solve: Simplifying 1 + -2w = 0 Solving 1 + -2w = 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 + -2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2w = 0 + -1 -2w = 0 + -1 Combine like terms: 0 + -1 = -1 -2w = -1 Divide each side by '-2'. w = 0.5 Simplifying w = 0.5Solution
w = {6, 0.5}
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