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Simplifying 5(r + -7) + 2[r + -3(r + -5)] = 0 Reorder the terms: 5(-7 + r) + 2[r + -3(r + -5)] = 0 (-7 * 5 + r * 5) + 2[r + -3(r + -5)] = 0 (-35 + 5r) + 2[r + -3(r + -5)] = 0 Reorder the terms: -35 + 5r + 2[r + -3(-5 + r)] = 0 -35 + 5r + 2[r + (-5 * -3 + r * -3)] = 0 -35 + 5r + 2[r + (15 + -3r)] = 0 Reorder the terms: -35 + 5r + 2[15 + r + -3r] = 0 Combine like terms: r + -3r = -2r -35 + 5r + 2[15 + -2r] = 0 -35 + 5r + [15 * 2 + -2r * 2] = 0 -35 + 5r + [30 + -4r] = 0 Reorder the terms: -35 + 30 + 5r + -4r = 0 Combine like terms: -35 + 30 = -5 -5 + 5r + -4r = 0 Combine like terms: 5r + -4r = 1r -5 + 1r = 0 Solving -5 + 1r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1r = 0 + 5 1r = 0 + 5 Combine like terms: 0 + 5 = 5 1r = 5 Divide each side by '1'. r = 5 Simplifying r = 5
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