Solve 2(2n+3)=6(5n+1)+2

$$2 ( 2 n + 3 ) = 6 ( 5 n + 1 ) + 2$$

Solve for n

$$n=-\frac{1}{13}\approx -0.076923077$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by 2n+3.

$$4n+6=6\left(5n+1\right)+2$$

Use the distributive property to multiply 6 by 5n+1.

$$4n+6=30n+6+2$$

Add 6 and 2 to get 8.

$$4n+6=30n+8$$

Subtract 30n from both sides.

$$4n+6-30n=8$$

Combine 4n and -30n to get -26n.

$$-26n+6=8$$

Subtract 6 from both sides.

$$-26n=8-6$$

Subtract 6 from 8 to get 2.

$$-26n=2$$

Divide both sides by -26.

$$n=\frac{2}{-26}$$

Reduce the fraction \frac{2}{-26} to lowest terms by extracting and canceling out 2.

$$n=-\frac{1}{13}$$