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Simplifying (3 + -1w)(2w + -7) = 0 Reorder the terms: (3 + -1w)(-7 + 2w) = 0 Multiply (3 + -1w) * (-7 + 2w) (3(-7 + 2w) + -1w * (-7 + 2w)) = 0 ((-7 * 3 + 2w * 3) + -1w * (-7 + 2w)) = 0 ((-21 + 6w) + -1w * (-7 + 2w)) = 0 (-21 + 6w + (-7 * -1w + 2w * -1w)) = 0 (-21 + 6w + (7w + -2w2)) = 0 Combine like terms: 6w + 7w = 13w (-21 + 13w + -2w2) = 0 Solving -21 + 13w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + 2w)(3 + -1w) = 0Subproblem 1
Set the factor '(-7 + 2w)' equal to zero and attempt to solve: Simplifying -7 + 2w = 0 Solving -7 + 2w = 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 + 2w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 2w = 0 + 7 2w = 0 + 7 Combine like terms: 0 + 7 = 7 2w = 7 Divide each side by '2'. w = 3.5 Simplifying w = 3.5Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {3.5, 3}
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