Solve for y square root of 15-5y=y-3

Math
15-5y=y-3
To remove the radical on the left side of the equation, square both sides of the equation.
15-5y2=(y-3)2
Simplify each side of the equation.
Tap for more steps…
Multiply the exponents in ((15-5y)12)2.
Tap for more steps…
Apply the power rule and multiply exponents, (am)n=amn.
(15-5y)12⋅2=(y-3)2
Cancel the common factor of 2.
Tap for more steps…
Cancel the common factor.
(15-5y)12⋅2=(y-3)2
Rewrite the expression.
(15-5y)1=(y-3)2
(15-5y)1=(y-3)2
(15-5y)1=(y-3)2
Simplify.
15-5y=(y-3)2
15-5y=(y-3)2
Solve for y.
Tap for more steps…
Simplify (y-3)2.
Tap for more steps…
Rewrite (y-3)2 as (y-3)(y-3).
15-5y=(y-3)(y-3)
Expand (y-3)(y-3) using the FOIL Method.
Tap for more steps…
Apply the distributive property.
15-5y=y(y-3)-3(y-3)
Apply the distributive property.
15-5y=y⋅y+y⋅-3-3(y-3)
Apply the distributive property.
15-5y=y⋅y+y⋅-3-3y-3⋅-3
15-5y=y⋅y+y⋅-3-3y-3⋅-3
Simplify and combine like terms.
Tap for more steps…
Simplify each term.
Tap for more steps…
Multiply y by y.
15-5y=y2+y⋅-3-3y-3⋅-3
Move -3 to the left of y.
15-5y=y2-3⋅y-3y-3⋅-3
Multiply -3 by -3.
15-5y=y2-3y-3y+9
15-5y=y2-3y-3y+9
Subtract 3y from -3y.
15-5y=y2-6y+9
15-5y=y2-6y+9
15-5y=y2-6y+9
Since y is on the right side of the equation, switch the sides so it is on the left side of the equation.
y2-6y+9=15-5y
Move all terms containing y to the left side of the equation.
Tap for more steps…
Add 5y to both sides of the equation.
y2-6y+9+5y=15
Add -6y and 5y.
y2-y+9=15
y2-y+9=15
Move 15 to the left side of the equation by subtracting it from both sides.
y2-y+9-15=0
Subtract 15 from 9.
y2-y-6=0
Factor y2-y-6 using the AC method.
Tap for more steps…
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -6 and whose sum is -1.
-3,2
Write the factored form using these integers.
(y-3)(y+2)=0
(y-3)(y+2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-3=0
y+2=0
Set the first factor equal to 0 and solve.
Tap for more steps…
Set the first factor equal to 0.
y-3=0
Add 3 to both sides of the equation.
y=3
y=3
Set the next factor equal to 0 and solve.
Tap for more steps…
Set the next factor equal to 0.
y+2=0
Subtract 2 from both sides of the equation.
y=-2
y=-2
The final solution is all the values that make (y-3)(y+2)=0 true.
y=3,-2
y=3,-2
Exclude the solutions that do not make 15-5y=y-3 true.
y=3
Solve for y square root of 15-5y=y-3

Solving MATH problems

We can solve all math problems. Get help on the web or with our math app

Scroll to top