Solve the following equality. 6(x-3)=19+6x

To solve the equation \(6(x-3) = 19 + 6x\), follow these steps:<br /><br />1. Distribute the 6 on the left side of the equation:<br /> \[<br /> 6 \cdot (x - 3) = 6x - 18<br /> \]<br /> So, the equation becomes:<br /> \[<br /> 6x - 18 = 19 + 6x<br /> \]<br /><br />2. Subtract \(6x\) from both sides to eliminate the \(6x\) term:<br /> \[<br /> 6x - 18 - 6x = 19 + 6x - 6x<br /> \]<br /> Simplifying gives:<br /> \[<br /> -18 = 19<br /> \]<br /><br />3. The resulting statement \(-18 = 19\) is a contradiction, which means there is no value of \(x\) that can satisfy the original equation.<br /><br />Therefore, the equation has no solution.