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Simplifying 4r + -3[4(3 + -3r) + -4(2 + -4r)] = 0 4r + -3[(3 * 4 + -3r * 4) + -4(2 + -4r)] = 0 4r + -3[(12 + -12r) + -4(2 + -4r)] = 0 4r + -3[12 + -12r + (2 * -4 + -4r * -4)] = 0 4r + -3[12 + -12r + (-8 + 16r)] = 0 Reorder the terms: 4r + -3[12 + -8 + -12r + 16r] = 0 Combine like terms: 12 + -8 = 4 4r + -3[4 + -12r + 16r] = 0 Combine like terms: -12r + 16r = 4r 4r + -3[4 + 4r] = 0 4r + [4 * -3 + 4r * -3] = 0 4r + [-12 + -12r] = 0 Reorder the terms: -12 + 4r + -12r = 0 Combine like terms: 4r + -12r = -8r -12 + -8r = 0 Solving -12 + -8r = 0 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -8r = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -8r = 0 + 12 -8r = 0 + 12 Combine like terms: 0 + 12 = 12 -8r = 12 Divide each side by '-8'. r = -1.5 Simplifying r = -1.5
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