5(2х-3)-2(3-2х)=15-6(х+1)

Let's solve the equation step by step:

The equation is: \[ 5(2x - 3) - 2(3 - 2x) = 15 - 6(x + 1) \]

First, expand the left-hand side: \[ 5(2x) - 5(3) - 2(3) + 2(2x) = 15 - 6(x + 1) \] \[ 10x - 15 - 6 + 4x = 15 - 6(x + 1) \] Combine the terms on the left: \[ 10x + 4x - 21 = 15 - 6(x + 1) \] \[ 14x - 21 = 15 - 6x - 6 \] Combine the constants on the right: \[ 14x - 21 = 9 - 6x \]

Next, we will add \(6x\) to both sides: \[ 14x + 6x - 21 = 9 \] Combine: \[ 20x - 21 = 9 \]

Now, add \(21\) to both sides: \[ 20x = 30 \]

Finally, divide by \(20\): \[ x = \frac{30}{20} = \frac{3}{2} \]

So the solution to the equation is: \[ x = \frac{3}{2} \]