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Simplifying (4w + -6)(7 + -1w) = 0 Reorder the terms: (-6 + 4w)(7 + -1w) = 0 Multiply (-6 + 4w) * (7 + -1w) (-6(7 + -1w) + 4w * (7 + -1w)) = 0 ((7 * -6 + -1w * -6) + 4w * (7 + -1w)) = 0 ((-42 + 6w) + 4w * (7 + -1w)) = 0 (-42 + 6w + (7 * 4w + -1w * 4w)) = 0 (-42 + 6w + (28w + -4w2)) = 0 Combine like terms: 6w + 28w = 34w (-42 + 34w + -4w2) = 0 Solving -42 + 34w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 17w + -2w2) = 0 Factor a trinomial. 2((-7 + w)(3 + -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 '(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 = {7, 1.5}
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