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Simplifying (5w + -6)(2w + 7) = 0 Reorder the terms: (-6 + 5w)(2w + 7) = 0 Reorder the terms: (-6 + 5w)(7 + 2w) = 0 Multiply (-6 + 5w) * (7 + 2w) (-6(7 + 2w) + 5w * (7 + 2w)) = 0 ((7 * -6 + 2w * -6) + 5w * (7 + 2w)) = 0 ((-42 + -12w) + 5w * (7 + 2w)) = 0 (-42 + -12w + (7 * 5w + 2w * 5w)) = 0 (-42 + -12w + (35w + 10w2)) = 0 Combine like terms: -12w + 35w = 23w (-42 + 23w + 10w2) = 0 Solving -42 + 23w + 10w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -2w)(6 + -5w) = 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 '(6 + -5w)' equal to zero and attempt to solve: Simplifying 6 + -5w = 0 Solving 6 + -5w = 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 + -5w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5w = 0 + -6 -5w = 0 + -6 Combine like terms: 0 + -6 = -6 -5w = -6 Divide each side by '-5'. w = 1.2 Simplifying w = 1.2Solution
w = {-3.5, 1.2}
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