Question

no solutions. -6(-6x - 6) = 36x + 36

Explanation:

Step1: Expand the left side

Using the distributive property \(a(b + c)=ab+ac\), for \(-6(-6x - 6)\), we have \((-6)\times(-6x)+(-6)\times(-6)=36x + 36\)

Step2: Compare both sides

The left side after expansion is \(36x + 36\) and the right side is also \(36x + 36\). This means the equation is an identity, and it has infinitely many solutions, not no solutions. But if we follow the process of solving:
Subtract \(36x\) from both sides: \(36x+36 - 36x=36x + 36-36x\)
Which simplifies to \(36 = 36\), a true statement for all \(x\).

Answer:

The equation \(-6(-6x - 6)=36x + 36\) has infinitely many solutions (the original claim of "no solutions" is incorrect). If we follow the solving steps, we end up with a true statement \(36 = 36\) which means all real numbers are solutions.