Classify the equation 12c + 5(5 + 3c) = 3(9c - 4) and state its solution.

1. Distribute on the left: 12c + 25 + 15c. 2. Combine like terms on the left: 27c + 25. 3. Distribute on the right: 27c - 12. 4. Subtract 27c from both sides: 25 = -12. 5. The variable terms vanish and what remains is false, so no value of c can ever satisfy the equation. 6. An equation that is false for all values of the variable is a contradiction, and a contradiction has no solution. 7. An identity would have left a true statement like 25 = 25, and a conditional equation would have kept a variable term, so both of those readings misclassify the algebra. _Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 2 "Solving Linear Equations and Inequalities", section 2.4 Use a General Strategy to Solve Linear Equations_