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Simplifying -5(3r + 8) + 6(4r + 10) = 0 Reorder the terms: -5(8 + 3r) + 6(4r + 10) = 0 (8 * -5 + 3r * -5) + 6(4r + 10) = 0 (-40 + -15r) + 6(4r + 10) = 0 Reorder the terms: -40 + -15r + 6(10 + 4r) = 0 -40 + -15r + (10 * 6 + 4r * 6) = 0 -40 + -15r + (60 + 24r) = 0 Reorder the terms: -40 + 60 + -15r + 24r = 0 Combine like terms: -40 + 60 = 20 20 + -15r + 24r = 0 Combine like terms: -15r + 24r = 9r 20 + 9r = 0 Solving 20 + 9r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + 9r = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 9r = 0 + -20 9r = 0 + -20 Combine like terms: 0 + -20 = -20 9r = -20 Divide each side by '9'. r = -2.222222222 Simplifying r = -2.222222222
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