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Simplifying 4(2r + 3) + -5(2r + 1) = 0 Reorder the terms: 4(3 + 2r) + -5(2r + 1) = 0 (3 * 4 + 2r * 4) + -5(2r + 1) = 0 (12 + 8r) + -5(2r + 1) = 0 Reorder the terms: 12 + 8r + -5(1 + 2r) = 0 12 + 8r + (1 * -5 + 2r * -5) = 0 12 + 8r + (-5 + -10r) = 0 Reorder the terms: 12 + -5 + 8r + -10r = 0 Combine like terms: 12 + -5 = 7 7 + 8r + -10r = 0 Combine like terms: 8r + -10r = -2r 7 + -2r = 0 Solving 7 + -2r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5
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