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Simplifying 2[3z + -5(2z + -3)] = 3z + -4 Reorder the terms: 2[3z + -5(-3 + 2z)] = 3z + -4 2[3z + (-3 * -5 + 2z * -5)] = 3z + -4 2[3z + (15 + -10z)] = 3z + -4 Reorder the terms: 2[15 + 3z + -10z] = 3z + -4 Combine like terms: 3z + -10z = -7z 2[15 + -7z] = 3z + -4 [15 * 2 + -7z * 2] = 3z + -4 [30 + -14z] = 3z + -4 Reorder the terms: 30 + -14z = -4 + 3z Solving 30 + -14z = -4 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 30 + -14z + -3z = -4 + 3z + -3z Combine like terms: -14z + -3z = -17z 30 + -17z = -4 + 3z + -3z Combine like terms: 3z + -3z = 0 30 + -17z = -4 + 0 30 + -17z = -4 Add '-30' to each side of the equation. 30 + -30 + -17z = -4 + -30 Combine like terms: 30 + -30 = 0 0 + -17z = -4 + -30 -17z = -4 + -30 Combine like terms: -4 + -30 = -34 -17z = -34 Divide each side by '-17'. z = 2 Simplifying z = 2
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