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

Math
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
Simplify each side of the equation.
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Multiply the exponents in ((6y+7)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(6y+7)12⋅2=4y+132
Cancel the common factor of 2.
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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.
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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.
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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
Solve for y.
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Move all terms containing y to the left side of the equation.
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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.
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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.
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Divide each term in 2y=6 by 2.
2y2=62
Cancel the common factor of 2.
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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

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