# Solve for y (5y-3)^2=9 (5y-3)2=9
Take the square root of each side of the equation to set up the solution for y
(5y-3)2⋅12=±9
Remove the perfect root factor 5y-3 under the radical to solve for y.
5y-3=±9
Simplify the right side of the equation.
Rewrite 9 as 32.
5y-3=±32
Pull terms out from under the radical, assuming positive real numbers.
5y-3=±3
5y-3=±3
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
5y-3=3
Move all terms not containing y to the right side of the equation.
Add 3 to both sides of the equation.
5y=3+3
Add 3 and 3.
5y=6
5y=6
Divide each term by 5 and simplify.
Divide each term in 5y=6 by 5.
5y5=65
Cancel the common factor of 5.
Cancel the common factor.
5y5=65
Divide y by 1.
y=65
y=65
y=65
Next, use the negative value of the ± to find the second solution.
5y-3=-3
Move all terms not containing y to the right side of the equation.
Add 3 to both sides of the equation.
5y=-3+3
Add -3 and 3.
5y=0
5y=0
Divide each term by 5 and simplify.
Divide each term in 5y=0 by 5.
5y5=05
Cancel the common factor of 5.
Cancel the common factor.
5y5=05
Divide y by 1.
y=05
y=05
Divide 0 by 5.
y=0
y=0
The complete solution is the result of both the positive and negative portions of the solution.
y=65,0
y=65,0
The result can be shown in multiple forms.
Exact Form:
y=65,0
Decimal Form:
y=1.2,0
Mixed Number Form:
y=115,0
Solve for y (5y-3)^2=9

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