Final answer:
The equation 6(x−6)=2(6+3x) simplifies to −36=12, which is not true. Hence, it has no solution.
Step-by-step explanation:
To solve the equation 6(x−6)=2(6+3x), we will start by distributing on both sides. On the left side, 6(x−6) becomes 6x−36, and on the right side, 2(6+3x) becomes 12+6x. So, the equation becomes 6x−36=12+6x.
Next, we will gather like terms. We can see that the variables and constants cancel out on both sides, leaving -36=12. Since -36 is not equal to 12, this equation has no solutions.
Therefore, the answer to the equation is non-solution.