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Simplifying 6(2 + 3) + -5(3z + 2) = 2(2z + -9) Combine like terms: 2 + 3 = 5 6(5) + -5(3z + 2) = 2(2z + -9) Multiply 6 * 5 30 + -5(3z + 2) = 2(2z + -9) Reorder the terms: 30 + -5(2 + 3z) = 2(2z + -9) 30 + (2 * -5 + 3z * -5) = 2(2z + -9) 30 + (-10 + -15z) = 2(2z + -9) Combine like terms: 30 + -10 = 20 20 + -15z = 2(2z + -9) Reorder the terms: 20 + -15z = 2(-9 + 2z) 20 + -15z = (-9 * 2 + 2z * 2) 20 + -15z = (-18 + 4z) Solving 20 + -15z = -18 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. 20 + -15z + -4z = -18 + 4z + -4z Combine like terms: -15z + -4z = -19z 20 + -19z = -18 + 4z + -4z Combine like terms: 4z + -4z = 0 20 + -19z = -18 + 0 20 + -19z = -18 Add '-20' to each side of the equation. 20 + -20 + -19z = -18 + -20 Combine like terms: 20 + -20 = 0 0 + -19z = -18 + -20 -19z = -18 + -20 Combine like terms: -18 + -20 = -38 -19z = -38 Divide each side by '-19'. z = 2 Simplifying z = 2
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