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Simplifying 10 + 3[2 + -8(3r + 4)] + 10(6r + -20) = 0 Reorder the terms: 10 + 3[2 + -8(4 + 3r)] + 10(6r + -20) = 0 10 + 3[2 + (4 * -8 + 3r * -8)] + 10(6r + -20) = 0 10 + 3[2 + (-32 + -24r)] + 10(6r + -20) = 0 Combine like terms: 2 + -32 = -30 10 + 3[-30 + -24r] + 10(6r + -20) = 0 10 + [-30 * 3 + -24r * 3] + 10(6r + -20) = 0 10 + [-90 + -72r] + 10(6r + -20) = 0 Reorder the terms: 10 + -90 + -72r + 10(-20 + 6r) = 0 10 + -90 + -72r + (-20 * 10 + 6r * 10) = 0 10 + -90 + -72r + (-200 + 60r) = 0 Reorder the terms: 10 + -90 + -200 + -72r + 60r = 0 Combine like terms: 10 + -90 = -80 -80 + -200 + -72r + 60r = 0 Combine like terms: -80 + -200 = -280 -280 + -72r + 60r = 0 Combine like terms: -72r + 60r = -12r -280 + -12r = 0 Solving -280 + -12r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '280' to each side of the equation. -280 + 280 + -12r = 0 + 280 Combine like terms: -280 + 280 = 0 0 + -12r = 0 + 280 -12r = 0 + 280 Combine like terms: 0 + 280 = 280 -12r = 280 Divide each side by '-12'. r = -23.33333333 Simplifying r = -23.33333333
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