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Simplifying 12 + -6(2r + -12) = -9(r + -12) + -6 Reorder the terms: 12 + -6(-12 + 2r) = -9(r + -12) + -6 12 + (-12 * -6 + 2r * -6) = -9(r + -12) + -6 12 + (72 + -12r) = -9(r + -12) + -6 Combine like terms: 12 + 72 = 84 84 + -12r = -9(r + -12) + -6 Reorder the terms: 84 + -12r = -9(-12 + r) + -6 84 + -12r = (-12 * -9 + r * -9) + -6 84 + -12r = (108 + -9r) + -6 Reorder the terms: 84 + -12r = 108 + -6 + -9r Combine like terms: 108 + -6 = 102 84 + -12r = 102 + -9r Solving 84 + -12r = 102 + -9r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '9r' to each side of the equation. 84 + -12r + 9r = 102 + -9r + 9r Combine like terms: -12r + 9r = -3r 84 + -3r = 102 + -9r + 9r Combine like terms: -9r + 9r = 0 84 + -3r = 102 + 0 84 + -3r = 102 Add '-84' to each side of the equation. 84 + -84 + -3r = 102 + -84 Combine like terms: 84 + -84 = 0 0 + -3r = 102 + -84 -3r = 102 + -84 Combine like terms: 102 + -84 = 18 -3r = 18 Divide each side by '-3'. r = -6 Simplifying r = -6
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