Solve -3(2x+1)-(x-3)=-2(x-1)+6x-(2-x)

$$- 3 ( 2 x + 1 ) - ( x - 3 ) = - 2 ( x - 1 ) + 6 x - ( 2 - x )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by 2x+1.

$$-6x-3-\left(x-3\right)=-2\left(x-1\right)+6x-\left(2-x\right)$$

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

$$-6x-3-x-\left(-3\right)=-2\left(x-1\right)+6x-\left(2-x\right)$$

The opposite of -3 is 3.

$$-6x-3-x+3=-2\left(x-1\right)+6x-\left(2-x\right)$$

Combine -6x and -x to get -7x.

$$-7x-3+3=-2\left(x-1\right)+6x-\left(2-x\right)$$

Add -3 and 3 to get 0.

$$-7x=-2\left(x-1\right)+6x-\left(2-x\right)$$

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

$$-7x=-2x+2+6x-\left(2-x\right)$$

Combine -2x and 6x to get 4x.

$$-7x=4x+2-\left(2-x\right)$$

To find the opposite of 2-x, find the opposite of each term.

$$-7x=4x+2-2-\left(-x\right)$$

The opposite of -x is x.

$$-7x=4x+2-2+x$$

Subtract 2 from 2 to get 0.

$$-7x=4x+x$$

Combine 4x and x to get 5x.

$$-7x=5x$$

Subtract 5x from both sides.

$$-7x-5x=0$$

Combine -7x and -5x to get -12x.

$$-12x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -12 is not equal to 0, x must be equal to 0.

$$x=0$$