5y2+2y=4y2-1

Subtract 4y2 from both sides of the equation.

5y2+2y-4y2=-1

Subtract 4y2 from 5y2.

y2+2y=-1

y2+2y=-1

Move 1 to the left side of the equation by adding it to both sides.

y2+2y+1=0

Rewrite 1 as 12.

y2+2y+12=0

Check the middle term by multiplying 2ab and compare this result with the middle term in the original expression.

2ab=2⋅y⋅1

Simplify.

2ab=2y

Factor using the perfect square trinomial rule a2+2ab+b2=(a+b)2, where a=y and b=1.

(y+1)2=0

(y+1)2=0

Set the y+1 equal to 0.

y+1=0

Subtract 1 from both sides of the equation.

y=-1

Solve for y 5y^2+2y=4y^2-1