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Simplifying 6(8z + -4) + -1[2(4z + -3) + 2] = 0 Reorder the terms: 6(-4 + 8z) + -1[2(4z + -3) + 2] = 0 (-4 * 6 + 8z * 6) + -1[2(4z + -3) + 2] = 0 (-24 + 48z) + -1[2(4z + -3) + 2] = 0 Reorder the terms: -24 + 48z + -1[2(-3 + 4z) + 2] = 0 -24 + 48z + -1[(-3 * 2 + 4z * 2) + 2] = 0 -24 + 48z + -1[(-6 + 8z) + 2] = 0 Reorder the terms: -24 + 48z + -1[-6 + 2 + 8z] = 0 Combine like terms: -6 + 2 = -4 -24 + 48z + -1[-4 + 8z] = 0 -24 + 48z + [-4 * -1 + 8z * -1] = 0 -24 + 48z + [4 + -8z] = 0 Reorder the terms: -24 + 4 + 48z + -8z = 0 Combine like terms: -24 + 4 = -20 -20 + 48z + -8z = 0 Combine like terms: 48z + -8z = 40z -20 + 40z = 0 Solving -20 + 40z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + 40z = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 40z = 0 + 20 40z = 0 + 20 Combine like terms: 0 + 20 = 20 40z = 20 Divide each side by '40'. z = 0.5 Simplifying z = 0.5
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