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Simplifying (14r + 9)(5r + -8) = 0 Reorder the terms: (9 + 14r)(5r + -8) = 0 Reorder the terms: (9 + 14r)(-8 + 5r) = 0 Multiply (9 + 14r) * (-8 + 5r) (9(-8 + 5r) + 14r * (-8 + 5r)) = 0 ((-8 * 9 + 5r * 9) + 14r * (-8 + 5r)) = 0 ((-72 + 45r) + 14r * (-8 + 5r)) = 0 (-72 + 45r + (-8 * 14r + 5r * 14r)) = 0 (-72 + 45r + (-112r + 70r2)) = 0 Combine like terms: 45r + -112r = -67r (-72 + -67r + 70r2) = 0 Solving -72 + -67r + 70r2 = 0 Solving for variable 'r'. Factor a trinomial. (-9 + -14r)(8 + -5r) = 0Subproblem 1
Set the factor '(-9 + -14r)' equal to zero and attempt to solve: Simplifying -9 + -14r = 0 Solving -9 + -14r = 0 Move all terms containing r to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -14r = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -14r = 0 + 9 -14r = 0 + 9 Combine like terms: 0 + 9 = 9 -14r = 9 Divide each side by '-14'. r = -0.6428571429 Simplifying r = -0.6428571429Subproblem 2
Set the factor '(8 + -5r)' equal to zero and attempt to solve: Simplifying 8 + -5r = 0 Solving 8 + -5r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5r = 0 + -8 -5r = 0 + -8 Combine like terms: 0 + -8 = -8 -5r = -8 Divide each side by '-5'. r = 1.6 Simplifying r = 1.6Solution
r = {-0.6428571429, 1.6}
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