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Simplifying (2 + w)(2w + -5) = 0 Reorder the terms: (2 + w)(-5 + 2w) = 0 Multiply (2 + w) * (-5 + 2w) (2(-5 + 2w) + w(-5 + 2w)) = 0 ((-5 * 2 + 2w * 2) + w(-5 + 2w)) = 0 ((-10 + 4w) + w(-5 + 2w)) = 0 (-10 + 4w + (-5 * w + 2w * w)) = 0 (-10 + 4w + (-5w + 2w2)) = 0 Combine like terms: 4w + -5w = -1w (-10 + -1w + 2w2) = 0 Solving -10 + -1w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-2 + -1w)(5 + -2w) = 0Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve: Simplifying -2 + -1w = 0 Solving -2 + -1w = 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 + -1w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1w = 0 + 2 -1w = 0 + 2 Combine like terms: 0 + 2 = 2 -1w = 2 Divide each side by '-1'. w = -2 Simplifying w = -2Subproblem 2
Set the factor '(5 + -2w)' equal to zero and attempt to solve: Simplifying 5 + -2w = 0 Solving 5 + -2w = 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 + -2w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2w = 0 + -5 -2w = 0 + -5 Combine like terms: 0 + -5 = -5 -2w = -5 Divide each side by '-2'. w = 2.5 Simplifying w = 2.5Solution
w = {-2, 2.5}
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