Solve 6x^3+2x^2+3x+2gx=5^2+x+1

$$6 { x }^{ 3 } +2 { x }^{ 2 } +3x+2gx = { 5 }^{ 2 } +x+1$$

Solve for g

$$g=-3x^{2}-x-1+\frac{13}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Calculate 5 to the power of 2 and get 25.

$$6x^{3}+2x^{2}+3x+2gx=25+x+1$$

Add 25 and 1 to get 26.

$$6x^{3}+2x^{2}+3x+2gx=26+x$$

Subtract 6x^{3} from both sides.

$$2x^{2}+3x+2gx=26+x-6x^{3}$$

Subtract 2x^{2} from both sides.

$$3x+2gx=26+x-6x^{3}-2x^{2}$$

Subtract 3x from both sides.

$$2gx=26+x-6x^{3}-2x^{2}-3x$$

Combine x and -3x to get -2x.

$$2gx=26-2x-6x^{3}-2x^{2}$$

The equation is in standard form.

$$2xg=26-2x-2x^{2}-6x^{3}$$

Divide both sides by 2x.

$$\frac{2xg}{2x}=\frac{26-2x-2x^{2}-6x^{3}}{2x}$$

Dividing by 2x undoes the multiplication by 2x.

$$g=\frac{26-2x-2x^{2}-6x^{3}}{2x}$$

Divide 26-2x-6x^{3}-2x^{2} by 2x.

$$g=-3x^{2}-x-1+\frac{13}{x}$$