Solve 4*0.5left(2+1right)+2left(2+1right)-6*1.5-3+x0.5*2*3+x0.866*2=0

$$4 \cdot 0.5 \left( 2+1 \right) +2 \left( 2+1 \right) -6 \cdot 1.5-3+x0.5 \cdot 2 \cdot 3+x0.866 \cdot 2=0$$

Solve for x_0

$$x_{0}=0$$

Steps for Solving Linear Equation

Multiply 4 and 0.5 to get 2.

$$2\left(2+1\right)+2\left(2+1\right)-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Add 2 and 1 to get 3.

$$2\times 3+2\left(2+1\right)-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Multiply 2 and 3 to get 6.

$$6+2\left(2+1\right)-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Add 2 and 1 to get 3.

$$6+2\times 3-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Multiply 2 and 3 to get 6.

$$6+6-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Add 6 and 6 to get 12.

$$12-6\times 1.5-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Multiply 6 and 1.5 to get 9.

$$12-9-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Subtract 9 from 12 to get 3.

$$3-3+x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Subtract 3 from 3 to get 0.

$$x_{0}\times 0.5\times 2\times 3+x_{0}\times 0.866\times 2=0$$

Multiply 0.5 and 2 to get 1.

$$x_{0}\times 3+x_{0}\times 0.866\times 2=0$$

Multiply 0.866 and 2 to get 1.732.

$$x_{0}\times 3+x_{0}\times 1.732=0$$

Combine x_{0}\times 3 and x_{0}\times 1.732 to get 4.732x_{0}.

$$4.732x_{0}=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 4.732 is not equal to 0, x_{0} must be equal to 0.

$$x_{0}=0$$