Solve (2x+1)+b*(2x+1)+3c*(2x+1)=(a

$$( 2 x + 1 ) + b \cdot ( 2 x + 1 ) + 3 c \cdot ( 2 x + 1 ) = ( a$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-\frac{6cx+2x+3c-a+1}{2x+1}\text{, }&x\neq -\frac{1}{2}\\b\in \mathrm{C}\text{, }&x=-\frac{1}{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2x+1+2bx+b+3c\left(2x+1\right)=a$$

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

$$2x+1+2bx+b+6cx+3c=a$$

Subtract 2x from both sides.

$$1+2bx+b+6cx+3c=a-2x$$

Subtract 1 from both sides.

$$2bx+b+6cx+3c=a-2x-1$$

Subtract 6cx from both sides.

$$2bx+b+3c=a-2x-1-6cx$$

Subtract 3c from both sides.

$$2bx+b=a-2x-1-6cx-3c$$

Combine all terms containing b.

$$\left(2x+1\right)b=a-2x-1-6cx-3c$$

The equation is in standard form.

$$\left(2x+1\right)b=-6cx-2x+a-3c-1$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)b}{2x+1}=\frac{-6cx-2x+a-3c-1}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$b=\frac{-6cx-2x+a-3c-1}{2x+1}$$

Solve for b

$$\left\{\begin{matrix}b=-\frac{6cx+2x+3c-a+1}{2x+1}\text{, }&x\neq -\frac{1}{2}\\b\in \mathrm{R}\text{, }&x=-\frac{1}{2}\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2x+1+2bx+b+3c\left(2x+1\right)=a$$

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

$$2x+1+2bx+b+6cx+3c=a$$

Subtract 2x from both sides.

$$1+2bx+b+6cx+3c=a-2x$$

Subtract 1 from both sides.

$$2bx+b+6cx+3c=a-2x-1$$

Subtract 6cx from both sides.

$$2bx+b+3c=a-2x-1-6cx$$

Subtract 3c from both sides.

$$2bx+b=a-2x-1-6cx-3c$$

Combine all terms containing b.

$$\left(2x+1\right)b=a-2x-1-6cx-3c$$

The equation is in standard form.

$$\left(2x+1\right)b=-6cx-2x+a-3c-1$$

Divide both sides by 1+2x.

$$\frac{\left(2x+1\right)b}{2x+1}=\frac{-6cx-2x+a-3c-1}{2x+1}$$

Dividing by 1+2x undoes the multiplication by 1+2x.

$$b=\frac{-6cx-2x+a-3c-1}{2x+1}$$

Solve for a

$$a=\left(2x+1\right)\left(b+3c+1\right)$$