11y+3-2y=0

Add 2y to both sides of the equation.

11y+3=2y

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

11y+32=(2y)2

Multiply the exponents in ((11y+3)12)2.

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

(11y+3)12⋅2=(2y)2

Cancel the common factor of 2.

Cancel the common factor.

(11y+3)12⋅2=(2y)2

Rewrite the expression.

(11y+3)1=(2y)2

(11y+3)1=(2y)2

(11y+3)1=(2y)2

Simplify.

11y+3=(2y)2

Apply the product rule to 2y.

11y+3=22y2

Raise 2 to the power of 2.

11y+3=4y2

11y+3=4y2

Subtract 4y2 from both sides of the equation.

11y+3-4y2=0

Factor the left side of the equation.

Factor -1 out of 11y+3-4y2.

Reorder the expression.

Move 3.

11y-4y2+3=0

Reorder 11y and -4y2.

-4y2+11y+3=0

-4y2+11y+3=0

Factor -1 out of -4y2.

-(4y2)+11y+3=0

Factor -1 out of 11y.

-(4y2)-(-11y)+3=0

Rewrite 3 as -1(-3).

-(4y2)-(-11y)-1⋅-3=0

Factor -1 out of -(4y2)-(-11y).

-(4y2-11y)-1⋅-3=0

Factor -1 out of -(4y2-11y)-1(-3).

-(4y2-11y-3)=0

-(4y2-11y-3)=0

Factor.

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-3=-12 and whose sum is b=-11.

Factor -11 out of -11y.

-(4y2-11y-3)=0

Rewrite -11 as 1 plus -12

-(4y2+(1-12)y-3)=0

Apply the distributive property.

-(4y2+1y-12y-3)=0

Multiply y by 1.

-(4y2+y-12y-3)=0

-(4y2+y-12y-3)=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

-((4y2+y)-12y-3)=0

Factor out the greatest common factor (GCF) from each group.

-(y(4y+1)-3(4y+1))=0

-(y(4y+1)-3(4y+1))=0

Factor the polynomial by factoring out the greatest common factor, 4y+1.

-((4y+1)(y-3))=0

-((4y+1)(y-3))=0

Remove unnecessary parentheses.

-(4y+1)(y-3)=0

-(4y+1)(y-3)=0

-(4y+1)(y-3)=0

Multiply each term in -(4y+1)(y-3)=0 by -1

Multiply each term in -(4y+1)(y-3)=0 by -1.

(-(4y+1)(y-3))⋅-1=0⋅-1

Simplify (-(4y+1)(y-3))⋅-1.

Simplify by multiplying through.

Apply the distributive property.

(-(4y)-1⋅1)(y-3)⋅-1=0⋅-1

Multiply.

Multiply 4 by -1.

(-4y-1⋅1)(y-3)⋅-1=0⋅-1

Multiply -1 by 1.

(-4y-1)(y-3)⋅-1=0⋅-1

(-4y-1)(y-3)⋅-1=0⋅-1

(-4y-1)(y-3)⋅-1=0⋅-1

Expand (-4y-1)(y-3) using the FOIL Method.

Apply the distributive property.

(-4y(y-3)-1(y-3))⋅-1=0⋅-1

Apply the distributive property.

(-4y⋅y-4y⋅-3-1(y-3))⋅-1=0⋅-1

Apply the distributive property.

(-4y⋅y-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1

(-4y⋅y-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1

Simplify and combine like terms.

Simplify each term.

Multiply y by y by adding the exponents.

Move y.

(-4(y⋅y)-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1

Multiply y by y.

(-4y2-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1

(-4y2-4y⋅-3-1y-1⋅-3)⋅-1=0⋅-1

Multiply -3 by -4.

(-4y2+12y-1y-1⋅-3)⋅-1=0⋅-1

Rewrite -1y as -y.

(-4y2+12y-y-1⋅-3)⋅-1=0⋅-1

Multiply -1 by -3.

(-4y2+12y-y+3)⋅-1=0⋅-1

(-4y2+12y-y+3)⋅-1=0⋅-1

Subtract y from 12y.

(-4y2+11y+3)⋅-1=0⋅-1

(-4y2+11y+3)⋅-1=0⋅-1

Apply the distributive property.

-4y2⋅-1+11y⋅-1+3⋅-1=0⋅-1

Simplify.

Multiply -1 by -4.

4y2+11y⋅-1+3⋅-1=0⋅-1

Multiply -1 by 11.

4y2-11y+3⋅-1=0⋅-1

Multiply 3 by -1.

4y2-11y-3=0⋅-1

4y2-11y-3=0⋅-1

4y2-11y-3=0⋅-1

Multiply 0 by -1.

4y2-11y-3=0

4y2-11y-3=0

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-3=-12 and whose sum is b=-11.

Factor -11 out of -11y.

4y2-11y-3=0

Rewrite -11 as 1 plus -12

4y2+(1-12)y-3=0

Apply the distributive property.

4y2+1y-12y-3=0

Multiply y by 1.

4y2+y-12y-3=0

4y2+y-12y-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(4y2+y)-12y-3=0

Factor out the greatest common factor (GCF) from each group.

y(4y+1)-3(4y+1)=0

y(4y+1)-3(4y+1)=0

Factor the polynomial by factoring out the greatest common factor, 4y+1.

(4y+1)(y-3)=0

(4y+1)(y-3)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

4y+1=0

y-3=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

4y+1=0

Subtract 1 from both sides of the equation.

4y=-1

Divide each term by 4 and simplify.

Divide each term in 4y=-1 by 4.

4y4=-14

Cancel the common factor of 4.

Cancel the common factor.

4y4=-14

Divide y by 1.

y=-14

y=-14

Move the negative in front of the fraction.

y=-14

y=-14

y=-14

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

y-3=0

Add 3 to both sides of the equation.

y=3

y=3

The final solution is all the values that make (4y+1)(y-3)=0 true.

y=-14,3

y=-14,3

Exclude the solutions that do not make 11y+3-2y=0 true.

y=3

Solve for y square root of 11y+3-2y=0