Let's solve the equation step by step:
The equation is: \[ 5(2x + 2) - 7x = 3x + 6 \]
First, distribute the \(5\) on the left side: \[ 10x + 10 - 7x = 3x + 6 \]
Combine like terms on the left side: \[ (10x - 7x) + 10 = 3x + 6 \] \[ 3x + 10 = 3x + 6 \]
Next, subtract \(3x\) from both sides: \[ 10 = 6 \]
This equation is a contradiction because \(10\) does not equal \(6\). Therefore, there are no values of \(x\) that can satisfy this equation.
Thus, the conclusion is: The equation has no solution.