Solve for \( x \) \( 2(6-2 x)+3 x=4+2(5+x) \)

To solve for \( x \), let's start by simplifying the equation step by step. The original equation is: \[ 2(6 - 2x) + 3x = 4 + 2(5 + x) \] First, we distribute the numbers outside the parentheses: \[ 12 - 4x + 3x = 4 + 10 + 2x \] Next, combine like terms on both sides: \[ 12 - x = 14 + 2x \] Now, we want to get all terms involving \( x \) on one side and constant terms on the other side. We can add \( x \) to both sides and subtract \( 14 \) from both sides: \[ 12 - 14 = 2x + x \] This simplifies to: \[ -2 = 3x \] Now, divide both sides by \( 3 \): \[ x = -\frac{2}{3} \] Thus, the solution is: \[ \boxed{-\frac{2}{3}} \]