6y+7-4y+13=0

Add 4y+13 to both sides of the equation.

6y+7=4y+13

To remove the radical on the left side of the equation, square both sides of the equation.

6y+72=4y+132

Multiply the exponents in ((6y+7)12)2.

Apply the power rule and multiply exponents, (am)n=amn.

(6y+7)12⋅2=4y+132

Cancel the common factor of 2.

Cancel the common factor.

(6y+7)12⋅2=4y+132

Rewrite the expression.

(6y+7)1=4y+132

(6y+7)1=4y+132

(6y+7)1=4y+132

Simplify.

6y+7=4y+132

Rewrite 4y+132 as 4y+13.

Use axn=axn to rewrite 4y+13 as (4y+13)12.

6y+7=((4y+13)12)2

Apply the power rule and multiply exponents, (am)n=amn.

6y+7=(4y+13)12⋅2

Combine 12 and 2.

6y+7=(4y+13)22

Cancel the common factor of 2.

Cancel the common factor.

6y+7=(4y+13)22

Divide 1 by 1.

6y+7=(4y+13)1

6y+7=(4y+13)1

Simplify.

6y+7=4y+13

6y+7=4y+13

6y+7=4y+13

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

Subtract 4y from both sides of the equation.

6y+7-4y=13

Subtract 4y from 6y.

2y+7=13

2y+7=13

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

Subtract 7 from both sides of the equation.

2y=13-7

Subtract 7 from 13.

2y=6

2y=6

Divide each term by 2 and simplify.

Divide each term in 2y=6 by 2.

2y2=62

Cancel the common factor of 2.

Cancel the common factor.

2y2=62

Divide y by 1.

y=62

y=62

Divide 6 by 2.

y=3

y=3

y=3

Solve for y square root of 6y+7- square root of 4y+13=0