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Simplifying (3w + -8)(9 + w) = 0 Reorder the terms: (-8 + 3w)(9 + w) = 0 Multiply (-8 + 3w) * (9 + w) (-8(9 + w) + 3w * (9 + w)) = 0 ((9 * -8 + w * -8) + 3w * (9 + w)) = 0 ((-72 + -8w) + 3w * (9 + w)) = 0 (-72 + -8w + (9 * 3w + w * 3w)) = 0 (-72 + -8w + (27w + 3w2)) = 0 Combine like terms: -8w + 27w = 19w (-72 + 19w + 3w2) = 0 Solving -72 + 19w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(8 + -3w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(8 + -3w)' equal to zero and attempt to solve: Simplifying 8 + -3w = 0 Solving 8 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3w = 0 + -8 -3w = 0 + -8 Combine like terms: 0 + -8 = -8 -3w = -8 Divide each side by '-3'. w = 2.666666667 Simplifying w = 2.666666667Solution
w = {-9, 2.666666667}
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