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Simplifying (9w + 7)(6w + -3) = 0 Reorder the terms: (7 + 9w)(6w + -3) = 0 Reorder the terms: (7 + 9w)(-3 + 6w) = 0 Multiply (7 + 9w) * (-3 + 6w) (7(-3 + 6w) + 9w * (-3 + 6w)) = 0 ((-3 * 7 + 6w * 7) + 9w * (-3 + 6w)) = 0 ((-21 + 42w) + 9w * (-3 + 6w)) = 0 (-21 + 42w + (-3 * 9w + 6w * 9w)) = 0 (-21 + 42w + (-27w + 54w2)) = 0 Combine like terms: 42w + -27w = 15w (-21 + 15w + 54w2) = 0 Solving -21 + 15w + 54w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + 5w + 18w2) = 0 Factor a trinomial. 3((-7 + -9w)(1 + -2w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -9w)' equal to zero and attempt to solve: Simplifying -7 + -9w = 0 Solving -7 + -9w = 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 + -9w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -9w = 0 + 7 -9w = 0 + 7 Combine like terms: 0 + 7 = 7 -9w = 7 Divide each side by '-9'. w = -0.7777777778 Simplifying w = -0.7777777778Subproblem 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 = {-0.7777777778, 0.5}
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