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Simplifying 12r + 7(3r + -5s) + -9(6r + 3s) + -2s = 0 12r + (3r * 7 + -5s * 7) + -9(6r + 3s) + -2s = 0 12r + (21r + -35s) + -9(6r + 3s) + -2s = 0 12r + 21r + -35s + (6r * -9 + 3s * -9) + -2s = 0 12r + 21r + -35s + (-54r + -27s) + -2s = 0 Reorder the terms: 12r + 21r + -54r + -35s + -27s + -2s = 0 Combine like terms: 12r + 21r = 33r 33r + -54r + -35s + -27s + -2s = 0 Combine like terms: 33r + -54r = -21r -21r + -35s + -27s + -2s = 0 Combine like terms: -35s + -27s = -62s -21r + -62s + -2s = 0 Combine like terms: -62s + -2s = -64s -21r + -64s = 0 Solving -21r + -64s = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '64s' to each side of the equation. -21r + -64s + 64s = 0 + 64s Combine like terms: -64s + 64s = 0 -21r + 0 = 0 + 64s -21r = 0 + 64s Remove the zero: -21r = 64s Divide each side by '-21'. r = -3.047619048s Simplifying r = -3.047619048s
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