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Simplifying 6(z + 3) + -5(3z + 3) = 2(2z + -9) Reorder the terms: 6(3 + z) + -5(3z + 3) = 2(2z + -9) (3 * 6 + z * 6) + -5(3z + 3) = 2(2z + -9) (18 + 6z) + -5(3z + 3) = 2(2z + -9) Reorder the terms: 18 + 6z + -5(3 + 3z) = 2(2z + -9) 18 + 6z + (3 * -5 + 3z * -5) = 2(2z + -9) 18 + 6z + (-15 + -15z) = 2(2z + -9) Reorder the terms: 18 + -15 + 6z + -15z = 2(2z + -9) Combine like terms: 18 + -15 = 3 3 + 6z + -15z = 2(2z + -9) Combine like terms: 6z + -15z = -9z 3 + -9z = 2(2z + -9) Reorder the terms: 3 + -9z = 2(-9 + 2z) 3 + -9z = (-9 * 2 + 2z * 2) 3 + -9z = (-18 + 4z) Solving 3 + -9z = -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. 3 + -9z + -4z = -18 + 4z + -4z Combine like terms: -9z + -4z = -13z 3 + -13z = -18 + 4z + -4z Combine like terms: 4z + -4z = 0 3 + -13z = -18 + 0 3 + -13z = -18 Add '-3' to each side of the equation. 3 + -3 + -13z = -18 + -3 Combine like terms: 3 + -3 = 0 0 + -13z = -18 + -3 -13z = -18 + -3 Combine like terms: -18 + -3 = -21 -13z = -21 Divide each side by '-13'. z = 1.615384615 Simplifying z = 1.615384615
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