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Simplifying 3 + 3(2z + -5) + -3(4z + 8) + -6 = 0 Reorder the terms: 3 + 3(-5 + 2z) + -3(4z + 8) + -6 = 0 3 + (-5 * 3 + 2z * 3) + -3(4z + 8) + -6 = 0 3 + (-15 + 6z) + -3(4z + 8) + -6 = 0 Reorder the terms: 3 + -15 + 6z + -3(8 + 4z) + -6 = 0 3 + -15 + 6z + (8 * -3 + 4z * -3) + -6 = 0 3 + -15 + 6z + (-24 + -12z) + -6 = 0 Reorder the terms: 3 + -15 + -24 + -6 + 6z + -12z = 0 Combine like terms: 3 + -15 = -12 -12 + -24 + -6 + 6z + -12z = 0 Combine like terms: -12 + -24 = -36 -36 + -6 + 6z + -12z = 0 Combine like terms: -36 + -6 = -42 -42 + 6z + -12z = 0 Combine like terms: 6z + -12z = -6z -42 + -6z = 0 Solving -42 + -6z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '42' to each side of the equation. -42 + 42 + -6z = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -6z = 0 + 42 -6z = 0 + 42 Combine like terms: 0 + 42 = 42 -6z = 42 Divide each side by '-6'. z = -7 Simplifying z = -7
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