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Simplifying 2w(9w + -2w)(2w + -1) = 0 Combine like terms: 9w + -2w = 7w 2w(7w)(2w + -1) = 0 Remove parenthesis around (7w) 2w * 7w(2w + -1) = 0 Reorder the terms: 2w * 7w(-1 + 2w) = 0 Reorder the terms for easier multiplication: 2 * 7w * w(-1 + 2w) = 0 Multiply 2 * 7 14w * w(-1 + 2w) = 0 Multiply w * w 14w2(-1 + 2w) = 0 (-1 * 14w2 + 2w * 14w2) = 0 (-14w2 + 28w3) = 0 Solving -14w2 + 28w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '14w2'. 14w2(-1 + 2w) = 0 Ignore the factor 14.Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve: Simplifying w2 = 0 Solving w2 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w2 = 0 Take the square root of each side: w = {0}Subproblem 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, 0.5}
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