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Simplifying 3(r + -10t) + -4(7t + 2r) = 0 (r * 3 + -10t * 3) + -4(7t + 2r) = 0 (3r + -30t) + -4(7t + 2r) = 0 Reorder the terms: 3r + -30t + -4(2r + 7t) = 0 3r + -30t + (2r * -4 + 7t * -4) = 0 3r + -30t + (-8r + -28t) = 0 Reorder the terms: 3r + -8r + -30t + -28t = 0 Combine like terms: 3r + -8r = -5r -5r + -30t + -28t = 0 Combine like terms: -30t + -28t = -58t -5r + -58t = 0 Solving -5r + -58t = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '58t' to each side of the equation. -5r + -58t + 58t = 0 + 58t Combine like terms: -58t + 58t = 0 -5r + 0 = 0 + 58t -5r = 0 + 58t Remove the zero: -5r = 58t Divide each side by '-5'. r = -11.6t Simplifying r = -11.6t
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