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Simplifying (7 + -1w)(4w + -2) = 0 Reorder the terms: (7 + -1w)(-2 + 4w) = 0 Multiply (7 + -1w) * (-2 + 4w) (7(-2 + 4w) + -1w * (-2 + 4w)) = 0 ((-2 * 7 + 4w * 7) + -1w * (-2 + 4w)) = 0 ((-14 + 28w) + -1w * (-2 + 4w)) = 0 (-14 + 28w + (-2 * -1w + 4w * -1w)) = 0 (-14 + 28w + (2w + -4w2)) = 0 Combine like terms: 28w + 2w = 30w (-14 + 30w + -4w2) = 0 Solving -14 + 30w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 15w + -2w2) = 0 Factor a trinomial. 2((-7 + w)(1 + -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 '(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 = {7, 0.5}
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