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Simplifying 8(r + 7t) + -4(13t + 5r) = 0 (r * 8 + 7t * 8) + -4(13t + 5r) = 0 (8r + 56t) + -4(13t + 5r) = 0 Reorder the terms: 8r + 56t + -4(5r + 13t) = 0 8r + 56t + (5r * -4 + 13t * -4) = 0 8r + 56t + (-20r + -52t) = 0 Reorder the terms: 8r + -20r + 56t + -52t = 0 Combine like terms: 8r + -20r = -12r -12r + 56t + -52t = 0 Combine like terms: 56t + -52t = 4t -12r + 4t = 0 Solving -12r + 4t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4t' to each side of the equation. -12r + 4t + -4t = 0 + -4t Combine like terms: 4t + -4t = 0 -12r + 0 = 0 + -4t -12r = 0 + -4t Remove the zero: -12r = -4t Divide each side by '-12'. r = 0.3333333333t Simplifying r = 0.3333333333t
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