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Simplifying 3(2z + -6) + -2(6z + 4) = 5(z + 8) Reorder the terms: 3(-6 + 2z) + -2(6z + 4) = 5(z + 8) (-6 * 3 + 2z * 3) + -2(6z + 4) = 5(z + 8) (-18 + 6z) + -2(6z + 4) = 5(z + 8) Reorder the terms: -18 + 6z + -2(4 + 6z) = 5(z + 8) -18 + 6z + (4 * -2 + 6z * -2) = 5(z + 8) -18 + 6z + (-8 + -12z) = 5(z + 8) Reorder the terms: -18 + -8 + 6z + -12z = 5(z + 8) Combine like terms: -18 + -8 = -26 -26 + 6z + -12z = 5(z + 8) Combine like terms: 6z + -12z = -6z -26 + -6z = 5(z + 8) Reorder the terms: -26 + -6z = 5(8 + z) -26 + -6z = (8 * 5 + z * 5) -26 + -6z = (40 + 5z) Solving -26 + -6z = 40 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -26 + -6z + -5z = 40 + 5z + -5z Combine like terms: -6z + -5z = -11z -26 + -11z = 40 + 5z + -5z Combine like terms: 5z + -5z = 0 -26 + -11z = 40 + 0 -26 + -11z = 40 Add '26' to each side of the equation. -26 + 26 + -11z = 40 + 26 Combine like terms: -26 + 26 = 0 0 + -11z = 40 + 26 -11z = 40 + 26 Combine like terms: 40 + 26 = 66 -11z = 66 Divide each side by '-11'. z = -6 Simplifying z = -6
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