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Simplifying -5(3r + 8) + 8(3r + 9) = 0 Reorder the terms: -5(8 + 3r) + 8(3r + 9) = 0 (8 * -5 + 3r * -5) + 8(3r + 9) = 0 (-40 + -15r) + 8(3r + 9) = 0 Reorder the terms: -40 + -15r + 8(9 + 3r) = 0 -40 + -15r + (9 * 8 + 3r * 8) = 0 -40 + -15r + (72 + 24r) = 0 Reorder the terms: -40 + 72 + -15r + 24r = 0 Combine like terms: -40 + 72 = 32 32 + -15r + 24r = 0 Combine like terms: -15r + 24r = 9r 32 + 9r = 0 Solving 32 + 9r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + 9r = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 9r = 0 + -32 9r = 0 + -32 Combine like terms: 0 + -32 = -32 9r = -32 Divide each side by '9'. r = -3.555555556 Simplifying r = -3.555555556
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