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Simplifying 2z + 3c + -8z + 4(z + -3) + c(2 + -3) = 0 Reorder the terms: 2z + 3c + -8z + 4(-3 + z) + c(2 + -3) = 0 2z + 3c + -8z + (-3 * 4 + z * 4) + c(2 + -3) = 0 2z + 3c + -8z + (-12 + 4z) + c(2 + -3) = 0 Combine like terms: 2 + -3 = -1 2z + 3c + -8z + -12 + 4z + c(-1) = 0 Reorder the terms for easier multiplication: 2z + 3c + -8z + -12 + 4z + -1c = 0 Reorder the terms: -12 + 3c + -1c + 2z + -8z + 4z = 0 Combine like terms: 3c + -1c = 2c -12 + 2c + 2z + -8z + 4z = 0 Combine like terms: 2z + -8z = -6z -12 + 2c + -6z + 4z = 0 Combine like terms: -6z + 4z = -2z -12 + 2c + -2z = 0 Solving -12 + 2c + -2z = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 2c + 12 + -2z = 0 + 12 Reorder the terms: -12 + 12 + 2c + -2z = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 2c + -2z = 0 + 12 2c + -2z = 0 + 12 Combine like terms: 0 + 12 = 12 2c + -2z = 12 Add '2z' to each side of the equation. 2c + -2z + 2z = 12 + 2z Combine like terms: -2z + 2z = 0 2c + 0 = 12 + 2z 2c = 12 + 2z Divide each side by '2'. c = 6 + z Simplifying c = 6 + z
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