Solve -2left(2left(x-1right)-x+2right)/5+-3left(3left(x+1right)+x-2right)/10=-3/10

$$\frac{ -2 \left( 2 \left( x-1 \right) -x+2 \right) }{ 5 } + \frac{ -3 \left( 3 \left( x+1 \right) +x-2 \right) }{ 10 } = - \frac{ 3 }{ 10 }$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,10.

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

Multiply 2 and -2 to get -4.

$$-4\left(2\left(x-1\right)-x+2\right)-3\left(3\left(x+1\right)+x-2\right)=-3$$

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

$$-4\left(2x-2-x+2\right)-3\left(3\left(x+1\right)+x-2\right)=-3$$

Combine 2x and -x to get x.

$$-4\left(x-2+2\right)-3\left(3\left(x+1\right)+x-2\right)=-3$$

Add -2 and 2 to get 0.

$$-4x-3\left(3\left(x+1\right)+x-2\right)=-3$$

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

$$-4x-3\left(3x+3+x-2\right)=-3$$

Combine 3x and x to get 4x.

$$-4x-3\left(4x+3-2\right)=-3$$

Subtract 2 from 3 to get 1.

$$-4x-3\left(4x+1\right)=-3$$

Use the distributive property to multiply -3 by 4x+1.

$$-4x-12x-3=-3$$

Combine -4x and -12x to get -16x.

$$-16x-3=-3$$

Add 3 to both sides.

$$-16x=-3+3$$

Add -3 and 3 to get 0.

$$-16x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -16 is not equal to 0, x must be equal to 0.

$$x=0$$