Solve 2x-3(x-2(x+1))=x-12-(x-3)

$$2 x - 3 ( x - 2 ( x + 1 ) ) = x - 12 - ( x - 3 )$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x+1.

$$2x-3\left(x-2x-2\right)=x-12-\left(x-3\right)$$

Combine x and -2x to get -x.

$$2x-3\left(-x-2\right)=x-12-\left(x-3\right)$$

Use the distributive property to multiply -3 by -x-2.

$$2x+3x+6=x-12-\left(x-3\right)$$

Combine 2x and 3x to get 5x.

$$5x+6=x-12-\left(x-3\right)$$

To find the opposite of x-3, find the opposite of each term.

$$5x+6=x-12-x-\left(-3\right)$$

The opposite of -3 is 3.

$$5x+6=x-12-x+3$$

Combine x and -x to get 0.

$$5x+6=-12+3$$

Add -12 and 3 to get -9.

$$5x+6=-9$$

Subtract 6 from both sides.

$$5x=-9-6$$

Subtract 6 from -9 to get -15.

$$5x=-15$$

Divide both sides by 5.

$$x=\frac{-15}{5}$$

Divide -15 by 5 to get -3.

$$x=-3$$