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Simplifying 9w(w + 8) + 8(8w + 9) = (8w + 9)(w + 8) Reorder the terms: 9w(8 + w) + 8(8w + 9) = (8w + 9)(w + 8) (8 * 9w + w * 9w) + 8(8w + 9) = (8w + 9)(w + 8) (72w + 9w2) + 8(8w + 9) = (8w + 9)(w + 8) Reorder the terms: 72w + 9w2 + 8(9 + 8w) = (8w + 9)(w + 8) 72w + 9w2 + (9 * 8 + 8w * 8) = (8w + 9)(w + 8) 72w + 9w2 + (72 + 64w) = (8w + 9)(w + 8) Reorder the terms: 72 + 72w + 64w + 9w2 = (8w + 9)(w + 8) Combine like terms: 72w + 64w = 136w 72 + 136w + 9w2 = (8w + 9)(w + 8) Reorder the terms: 72 + 136w + 9w2 = (9 + 8w)(w + 8) Reorder the terms: 72 + 136w + 9w2 = (9 + 8w)(8 + w) Multiply (9 + 8w) * (8 + w) 72 + 136w + 9w2 = (9(8 + w) + 8w * (8 + w)) 72 + 136w + 9w2 = ((8 * 9 + w * 9) + 8w * (8 + w)) 72 + 136w + 9w2 = ((72 + 9w) + 8w * (8 + w)) 72 + 136w + 9w2 = (72 + 9w + (8 * 8w + w * 8w)) 72 + 136w + 9w2 = (72 + 9w + (64w + 8w2)) Combine like terms: 9w + 64w = 73w 72 + 136w + 9w2 = (72 + 73w + 8w2) Add '-72' to each side of the equation. 72 + 136w + -72 + 9w2 = 72 + 73w + -72 + 8w2 Reorder the terms: 72 + -72 + 136w + 9w2 = 72 + 73w + -72 + 8w2 Combine like terms: 72 + -72 = 0 0 + 136w + 9w2 = 72 + 73w + -72 + 8w2 136w + 9w2 = 72 + 73w + -72 + 8w2 Reorder the terms: 136w + 9w2 = 72 + -72 + 73w + 8w2 Combine like terms: 72 + -72 = 0 136w + 9w2 = 0 + 73w + 8w2 136w + 9w2 = 73w + 8w2 Solving 136w + 9w2 = 73w + 8w2 Solving for variable 'w'. Reorder the terms: 136w + -73w + 9w2 + -8w2 = 73w + 8w2 + -73w + -8w2 Combine like terms: 136w + -73w = 63w 63w + 9w2 + -8w2 = 73w + 8w2 + -73w + -8w2 Combine like terms: 9w2 + -8w2 = 1w2 63w + 1w2 = 73w + 8w2 + -73w + -8w2 Reorder the terms: 63w + 1w2 = 73w + -73w + 8w2 + -8w2 Combine like terms: 73w + -73w = 0 63w + 1w2 = 0 + 8w2 + -8w2 63w + 1w2 = 8w2 + -8w2 Combine like terms: 8w2 + -8w2 = 0 63w + 1w2 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(63 + w) = 0Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
Set the factor '(63 + w)' equal to zero and attempt to solve: Simplifying 63 + w = 0 Solving 63 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-63' to each side of the equation. 63 + -63 + w = 0 + -63 Combine like terms: 63 + -63 = 0 0 + w = 0 + -63 w = 0 + -63 Combine like terms: 0 + -63 = -63 w = -63 Simplifying w = -63Solution
w = {0, -63}
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