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Simplifying -7(5r + 3) + 9(10R + 7) = 0 Reorder the terms: -7(3 + 5r) + 9(10R + 7) = 0 (3 * -7 + 5r * -7) + 9(10R + 7) = 0 (-21 + -35r) + 9(10R + 7) = 0 Reorder the terms: -21 + -35r + 9(7 + 10R) = 0 -21 + -35r + (7 * 9 + 10R * 9) = 0 -21 + -35r + (63 + 90R) = 0 Reorder the terms: -21 + 63 + 90R + -35r = 0 Combine like terms: -21 + 63 = 42 42 + 90R + -35r = 0 Solving 42 + 90R + -35r = 0 Solving for variable 'R'. Move all terms containing R to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + 90R + -42 + -35r = 0 + -42 Reorder the terms: 42 + -42 + 90R + -35r = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 90R + -35r = 0 + -42 90R + -35r = 0 + -42 Combine like terms: 0 + -42 = -42 90R + -35r = -42 Add '35r' to each side of the equation. 90R + -35r + 35r = -42 + 35r Combine like terms: -35r + 35r = 0 90R + 0 = -42 + 35r 90R = -42 + 35r Divide each side by '90'. R = -0.4666666667 + 0.3888888889r Simplifying R = -0.4666666667 + 0.3888888889r
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