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Simplifying 8 + r + r + -12 = -1(12 + -3r) + 4(9r + 2) Reorder the terms: 8 + -12 + r + r = -1(12 + -3r) + 4(9r + 2) Combine like terms: 8 + -12 = -4 -4 + r + r = -1(12 + -3r) + 4(9r + 2) Combine like terms: r + r = 2r -4 + 2r = -1(12 + -3r) + 4(9r + 2) -4 + 2r = (12 * -1 + -3r * -1) + 4(9r + 2) -4 + 2r = (-12 + 3r) + 4(9r + 2) Reorder the terms: -4 + 2r = -12 + 3r + 4(2 + 9r) -4 + 2r = -12 + 3r + (2 * 4 + 9r * 4) -4 + 2r = -12 + 3r + (8 + 36r) Reorder the terms: -4 + 2r = -12 + 8 + 3r + 36r Combine like terms: -12 + 8 = -4 -4 + 2r = -4 + 3r + 36r Combine like terms: 3r + 36r = 39r -4 + 2r = -4 + 39r Add '4' to each side of the equation. -4 + 4 + 2r = -4 + 4 + 39r Combine like terms: -4 + 4 = 0 0 + 2r = -4 + 4 + 39r 2r = -4 + 4 + 39r Combine like terms: -4 + 4 = 0 2r = 0 + 39r 2r = 39r Solving 2r = 39r Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-39r' to each side of the equation. 2r + -39r = 39r + -39r Combine like terms: 2r + -39r = -37r -37r = 39r + -39r Combine like terms: 39r + -39r = 0 -37r = 0 Divide each side by '-37'. r = 0 Simplifying r = 0
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