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Simplifying (2r + -5)(r + -10) = 0 Reorder the terms: (-5 + 2r)(r + -10) = 0 Reorder the terms: (-5 + 2r)(-10 + r) = 0 Multiply (-5 + 2r) * (-10 + r) (-5(-10 + r) + 2r * (-10 + r)) = 0 ((-10 * -5 + r * -5) + 2r * (-10 + r)) = 0 ((50 + -5r) + 2r * (-10 + r)) = 0 (50 + -5r + (-10 * 2r + r * 2r)) = 0 (50 + -5r + (-20r + 2r2)) = 0 Combine like terms: -5r + -20r = -25r (50 + -25r + 2r2) = 0 Solving 50 + -25r + 2r2 = 0 Solving for variable 'r'. Factor a trinomial. (5 + -2r)(10 + -1r) = 0Subproblem 1
Set the factor '(5 + -2r)' equal to zero and attempt to solve: Simplifying 5 + -2r = 0 Solving 5 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2r = 0 + -5 -2r = 0 + -5 Combine like terms: 0 + -5 = -5 -2r = -5 Divide each side by '-2'. r = 2.5 Simplifying r = 2.5Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve: Simplifying 10 + -1r = 0 Solving 10 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1r = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1r = 0 + -10 -1r = 0 + -10 Combine like terms: 0 + -10 = -10 -1r = -10 Divide each side by '-1'. r = 10 Simplifying r = 10Solution
r = {2.5, 10}
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