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Simplifying (5 + -1w)(5w + -3) = 0 Reorder the terms: (5 + -1w)(-3 + 5w) = 0 Multiply (5 + -1w) * (-3 + 5w) (5(-3 + 5w) + -1w * (-3 + 5w)) = 0 ((-3 * 5 + 5w * 5) + -1w * (-3 + 5w)) = 0 ((-15 + 25w) + -1w * (-3 + 5w)) = 0 (-15 + 25w + (-3 * -1w + 5w * -1w)) = 0 (-15 + 25w + (3w + -5w2)) = 0 Combine like terms: 25w + 3w = 28w (-15 + 28w + -5w2) = 0 Solving -15 + 28w + -5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + w)(3 + -5w) = 0Subproblem 1
Set the factor '(-5 + w)' equal to zero and attempt to solve: Simplifying -5 + w = 0 Solving -5 + w = 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 + w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + w = 0 + 5 w = 0 + 5 Combine like terms: 0 + 5 = 5 w = 5 Simplifying w = 5Subproblem 2
Set the factor '(3 + -5w)' equal to zero and attempt to solve: Simplifying 3 + -5w = 0 Solving 3 + -5w = 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 + -5w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5w = 0 + -3 -5w = 0 + -3 Combine like terms: 0 + -3 = -3 -5w = -3 Divide each side by '-5'. w = 0.6 Simplifying w = 0.6Solution
w = {5, 0.6}
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