4(2x+3)=12(x-2)

To solve the equation \( 4(2x + 3) = 12(x - 2) \), we will first distribute the terms on both sides. Starting with the left side: \[ 4(2x + 3) = 8x + 12 \] Now, for the right side: \[ 12(x - 2) = 12x - 24 \] Now, we can rewrite the equation: \[ 8x + 12 = 12x - 24 \] Next, we will move all the terms involving \( x \) to one side and the constant terms to the other. Subtract \( 8x \) from both sides: \[ 12 = 12x - 8x - 24 \] This simplifies to: \[ 12 = 4x - 24 \] Next, add \( 24 \) to both sides: \[ 12 + 24 = 4x \] \[ 36 = 4x \] Now, divide both sides by \( 4 \): \[ x = \frac{36}{4} = 9 \] Thus, the solution to the equation \( 4(2x + 3) = 12(x - 2) \) is: \[ \boxed{9} \]