Let's solve the equation step by step:
Given equation: \[ 3(2x + 2) - 10x = -4x + 6 \]
Step 1: Distribute the left side. \[ 3 \times 2x + 3 \times 2 - 10x = -4x + 6 \] \[ 6x + 6 - 10x = -4x + 6 \]
Step 2: Combine like terms on the left side. \[ (6x - 10x) + 6 = -4x + 6 \] \[ -4x + 6 = -4x + 6 \]
Step 3: Isolate variable terms. Now we see that both sides of the equation are identical: \[ -4x + 6 = -4x + 6 \]
This means that the equation is true for all values of \( x \).
Conclusion: The equation has infinite solutions. Every value of \( x \) will satisfy the equation.