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Simplifying (7w + 5)(2w + -6) = 0 Reorder the terms: (5 + 7w)(2w + -6) = 0 Reorder the terms: (5 + 7w)(-6 + 2w) = 0 Multiply (5 + 7w) * (-6 + 2w) (5(-6 + 2w) + 7w * (-6 + 2w)) = 0 ((-6 * 5 + 2w * 5) + 7w * (-6 + 2w)) = 0 ((-30 + 10w) + 7w * (-6 + 2w)) = 0 (-30 + 10w + (-6 * 7w + 2w * 7w)) = 0 (-30 + 10w + (-42w + 14w2)) = 0 Combine like terms: 10w + -42w = -32w (-30 + -32w + 14w2) = 0 Solving -30 + -32w + 14w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -16w + 7w2) = 0 Factor a trinomial. 2((-5 + -7w)(3 + -1w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -7w)' equal to zero and attempt to solve: Simplifying -5 + -7w = 0 Solving -5 + -7w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7w = 0 + 5 -7w = 0 + 5 Combine like terms: 0 + 5 = 5 -7w = 5 Divide each side by '-7'. w = -0.7142857143 Simplifying w = -0.7142857143Subproblem 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 = {-0.7142857143, 3}
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