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Simplifying (5 + w)(5w + -2) = 0 Reorder the terms: (5 + w)(-2 + 5w) = 0 Multiply (5 + w) * (-2 + 5w) (5(-2 + 5w) + w(-2 + 5w)) = 0 ((-2 * 5 + 5w * 5) + w(-2 + 5w)) = 0 ((-10 + 25w) + w(-2 + 5w)) = 0 (-10 + 25w + (-2 * w + 5w * w)) = 0 (-10 + 25w + (-2w + 5w2)) = 0 Combine like terms: 25w + -2w = 23w (-10 + 23w + 5w2) = 0 Solving -10 + 23w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(2 + -5w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(2 + -5w)' equal to zero and attempt to solve: Simplifying 2 + -5w = 0 Solving 2 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5w = 0 + -2 -5w = 0 + -2 Combine like terms: 0 + -2 = -2 -5w = -2 Divide each side by '-5'. w = 0.4 Simplifying w = 0.4Solution
w = {-5, 0.4}
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