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Simplifying z * 3 + 5(z + 3) + -4(2 + -2z * 2) = 0 Reorder the terms for easier multiplication: 3z + 5(z + 3) + -4(2 + -2z * 2) = 0 Reorder the terms: 3z + 5(3 + z) + -4(2 + -2z * 2) = 0 3z + (3 * 5 + z * 5) + -4(2 + -2z * 2) = 0 3z + (15 + 5z) + -4(2 + -2z * 2) = 0 Reorder the terms for easier multiplication: 3z + 15 + 5z + -4(2 + -2 * 2z) = 0 Multiply -2 * 2 3z + 15 + 5z + -4(2 + -4z) = 0 3z + 15 + 5z + (2 * -4 + -4z * -4) = 0 3z + 15 + 5z + (-8 + 16z) = 0 Reorder the terms: 15 + -8 + 3z + 5z + 16z = 0 Combine like terms: 15 + -8 = 7 7 + 3z + 5z + 16z = 0 Combine like terms: 3z + 5z = 8z 7 + 8z + 16z = 0 Combine like terms: 8z + 16z = 24z 7 + 24z = 0 Solving 7 + 24z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 24z = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 24z = 0 + -7 24z = 0 + -7 Combine like terms: 0 + -7 = -7 24z = -7 Divide each side by '24'. z = -0.2916666667 Simplifying z = -0.2916666667
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