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Simplifying -10 + -1(2z + 1) + 12z + -3(2z + 1) = 5(3z + -5) Reorder the terms: -10 + -1(1 + 2z) + 12z + -3(2z + 1) = 5(3z + -5) -10 + (1 * -1 + 2z * -1) + 12z + -3(2z + 1) = 5(3z + -5) -10 + (-1 + -2z) + 12z + -3(2z + 1) = 5(3z + -5) Reorder the terms: -10 + -1 + -2z + 12z + -3(1 + 2z) = 5(3z + -5) -10 + -1 + -2z + 12z + (1 * -3 + 2z * -3) = 5(3z + -5) -10 + -1 + -2z + 12z + (-3 + -6z) = 5(3z + -5) Reorder the terms: -10 + -1 + -3 + -2z + 12z + -6z = 5(3z + -5) Combine like terms: -10 + -1 = -11 -11 + -3 + -2z + 12z + -6z = 5(3z + -5) Combine like terms: -11 + -3 = -14 -14 + -2z + 12z + -6z = 5(3z + -5) Combine like terms: -2z + 12z = 10z -14 + 10z + -6z = 5(3z + -5) Combine like terms: 10z + -6z = 4z -14 + 4z = 5(3z + -5) Reorder the terms: -14 + 4z = 5(-5 + 3z) -14 + 4z = (-5 * 5 + 3z * 5) -14 + 4z = (-25 + 15z) Solving -14 + 4z = -25 + 15z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15z' to each side of the equation. -14 + 4z + -15z = -25 + 15z + -15z Combine like terms: 4z + -15z = -11z -14 + -11z = -25 + 15z + -15z Combine like terms: 15z + -15z = 0 -14 + -11z = -25 + 0 -14 + -11z = -25 Add '14' to each side of the equation. -14 + 14 + -11z = -25 + 14 Combine like terms: -14 + 14 = 0 0 + -11z = -25 + 14 -11z = -25 + 14 Combine like terms: -25 + 14 = -11 -11z = -11 Divide each side by '-11'. z = 1 Simplifying z = 1
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