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Simplifying 6[4(z + -5) + 17] + -1[2(4z + -3) + 1] = 0 Reorder the terms: 6[4(-5 + z) + 17] + -1[2(4z + -3) + 1] = 0 6[(-5 * 4 + z * 4) + 17] + -1[2(4z + -3) + 1] = 0 6[(-20 + 4z) + 17] + -1[2(4z + -3) + 1] = 0 Reorder the terms: 6[-20 + 17 + 4z] + -1[2(4z + -3) + 1] = 0 Combine like terms: -20 + 17 = -3 6[-3 + 4z] + -1[2(4z + -3) + 1] = 0 [-3 * 6 + 4z * 6] + -1[2(4z + -3) + 1] = 0 [-18 + 24z] + -1[2(4z + -3) + 1] = 0 Reorder the terms: -18 + 24z + -1[2(-3 + 4z) + 1] = 0 -18 + 24z + -1[(-3 * 2 + 4z * 2) + 1] = 0 -18 + 24z + -1[(-6 + 8z) + 1] = 0 Reorder the terms: -18 + 24z + -1[-6 + 1 + 8z] = 0 Combine like terms: -6 + 1 = -5 -18 + 24z + -1[-5 + 8z] = 0 -18 + 24z + [-5 * -1 + 8z * -1] = 0 -18 + 24z + [5 + -8z] = 0 Reorder the terms: -18 + 5 + 24z + -8z = 0 Combine like terms: -18 + 5 = -13 -13 + 24z + -8z = 0 Combine like terms: 24z + -8z = 16z -13 + 16z = 0 Solving -13 + 16z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + 16z = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 16z = 0 + 13 16z = 0 + 13 Combine like terms: 0 + 13 = 13 16z = 13 Divide each side by '16'. z = 0.8125 Simplifying z = 0.8125
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