|2a+6|=|3a-6|

Rewrite the absolute value equation as four equations without absolute value bars.

2a+6=3a-6

2a+6=-(3a-6)

-(2a+6)=3a-6

-(2a+6)=-(3a-6)

After simplifying, there are only two unique equations to be solved.

2a+6=3a-6

2a+6=-(3a-6)

Move all terms containing a to the left side of the equation.

Subtract 3a from both sides of the equation.

2a+6-3a=-6

Subtract 3a from 2a.

-a+6=-6

-a+6=-6

Move all terms not containing a to the right side of the equation.

Subtract 6 from both sides of the equation.

-a=-6-6

Subtract 6 from -6.

-a=-12

-a=-12

Multiply each term in -a=-12 by -1

Multiply each term in -a=-12 by -1.

(-a)⋅-1=(-12)⋅-1

Multiply (-a)⋅-1.

Multiply -1 by -1.

1a=(-12)⋅-1

Multiply a by 1.

a=(-12)⋅-1

a=(-12)⋅-1

Multiply -12 by -1.

a=12

a=12

a=12

Simplify -(3a-6).

Apply the distributive property.

2a+6=-(3a)–6

Multiply.

Multiply 3 by -1.

2a+6=-3a–6

Multiply -1 by -6.

2a+6=-3a+6

2a+6=-3a+6

2a+6=-3a+6

Move all terms containing a to the left side of the equation.

Add 3a to both sides of the equation.

2a+6+3a=6

Add 2a and 3a.

5a+6=6

5a+6=6

Move all terms not containing a to the right side of the equation.

Subtract 6 from both sides of the equation.

5a=6-6

Subtract 6 from 6.

5a=0

5a=0

Divide each term by 5 and simplify.

Divide each term in 5a=0 by 5.

5a5=05

Cancel the common factor of 5.

Cancel the common factor.

5a5=05

Divide a by 1.

a=05

a=05

Divide 0 by 5.

a=0

a=0

a=0

List all of the solutions.

a=12,0

Solve for a |2a+6|=|3a-6|