Solve n2(x+3)-(2x-7)=12

$$n 2 ( x + 3 ) - ( 2 x - 7 ) = 12$$

Solve for n_2

$$n_{2}=\frac{2x+5}{x+3}$$

$$x\neq -3$$

Steps for Solving Linear Equation

Use the distributive property to multiply n_{2} by x+3.

$$n_{2}x+3n_{2}-\left(2x-7\right)=12$$

To find the opposite of 2x-7, find the opposite of each term.

$$n_{2}x+3n_{2}-2x+7=12$$

Add 2x to both sides.

$$n_{2}x+3n_{2}+7=12+2x$$

Subtract 7 from both sides.

$$n_{2}x+3n_{2}=12+2x-7$$

Subtract 7 from 12 to get 5.

$$n_{2}x+3n_{2}=5+2x$$

Combine all terms containing n_{2}.

$$\left(x+3\right)n_{2}=5+2x$$

The equation is in standard form.

$$\left(x+3\right)n_{2}=2x+5$$

Divide both sides by x+3.

$$\frac{\left(x+3\right)n_{2}}{x+3}=\frac{2x+5}{x+3}$$

Dividing by x+3 undoes the multiplication by x+3.

$$n_{2}=\frac{2x+5}{x+3}$$

Solve for x

$$x=-\frac{3n_{2}-5}{n_{2}-2}$$

$$n_{2}\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply n_{2} by x+3.

$$n_{2}x+3n_{2}-\left(2x-7\right)=12$$

To find the opposite of 2x-7, find the opposite of each term.

$$n_{2}x+3n_{2}-2x+7=12$$

Subtract 3n_{2} from both sides.

$$n_{2}x-2x+7=12-3n_{2}$$

Subtract 7 from both sides.

$$n_{2}x-2x=12-3n_{2}-7$$

Subtract 7 from 12 to get 5.

$$n_{2}x-2x=5-3n_{2}$$

Combine all terms containing x.

$$\left(n_{2}-2\right)x=5-3n_{2}$$

Divide both sides by n_{2}-2.

$$\frac{\left(n_{2}-2\right)x}{n_{2}-2}=\frac{5-3n_{2}}{n_{2}-2}$$

Dividing by n_{2}-2 undoes the multiplication by n_{2}-2.

$$x=\frac{5-3n_{2}}{n_{2}-2}$$