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Simplifying (6 + -1w)(2w + -9) = 0 Reorder the terms: (6 + -1w)(-9 + 2w) = 0 Multiply (6 + -1w) * (-9 + 2w) (6(-9 + 2w) + -1w * (-9 + 2w)) = 0 ((-9 * 6 + 2w * 6) + -1w * (-9 + 2w)) = 0 ((-54 + 12w) + -1w * (-9 + 2w)) = 0 (-54 + 12w + (-9 * -1w + 2w * -1w)) = 0 (-54 + 12w + (9w + -2w2)) = 0 Combine like terms: 12w + 9w = 21w (-54 + 21w + -2w2) = 0 Solving -54 + 21w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-6 + w)(9 + -2w) = 0Subproblem 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 '(9 + -2w)' equal to zero and attempt to solve: Simplifying 9 + -2w = 0 Solving 9 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2w = 0 + -9 -2w = 0 + -9 Combine like terms: 0 + -9 = -9 -2w = -9 Divide each side by '-2'. w = 4.5 Simplifying w = 4.5Solution
w = {6, 4.5}
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