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Simplifying 5(3 + 2r) + -3(-10 + -1r) = 0 (3 * 5 + 2r * 5) + -3(-10 + -1r) = 0 (15 + 10r) + -3(-10 + -1r) = 0 15 + 10r + (-10 * -3 + -1r * -3) = 0 15 + 10r + (30 + 3r) = 0 Reorder the terms: 15 + 30 + 10r + 3r = 0 Combine like terms: 15 + 30 = 45 45 + 10r + 3r = 0 Combine like terms: 10r + 3r = 13r 45 + 13r = 0 Solving 45 + 13r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 13r = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 13r = 0 + -45 13r = 0 + -45 Combine like terms: 0 + -45 = -45 13r = -45 Divide each side by '13'. r = -3.461538462 Simplifying r = -3.461538462
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