The equation is solved step by step, resulting in x = 12/11 as the solution for the variable x.
Start with the given equation: 6(x+3) = 5(6-x).
Distribute the 6 on the left side and the 5 on the right side: 6x + 18 = 30 - 5x.
Subtract 18 from both sides to isolate the terms containing x: 6x + 18 -18 = 30 - 18 - 5x.
Combine like terms by adding 5x to both sides: 6x = 12 -5x.
Add 5x to both sides to consolidate x terms on one side: 6x + 5x = 12 - 5x + 5x.
Combine like terms on both sides: 11x = 12.
Divide both sides by 11 to solve for x: x = 12/11.
In summary, the step-by-step solution involves simplifying and manipulating the equation to isolate the variable x. The final solution is x = 12/11.