# Solve for y r=2y^2+2y-1

r=2y2+2y-1
Rewrite the equation as 2y2+2y-1=r.
2y2+2y-1=r
Move r to the left side of the equation by subtracting it from both sides.
2y2+2y-1-r=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=2, b=2, and c=-1-r into the quadratic formula and solve for y.
-2±22-4⋅(2⋅(-1-r))2⋅2
Simplify.
Simplify the numerator.
Factor 2 out of 22-4⋅(2⋅(-1-r)).
Factor 2 out of 22.
y=-2±2⋅2-4⋅(2⋅(-1-r))2⋅2
Factor 2 out of -4⋅(2⋅(-1-r)).
y=-2±2⋅2+2(-2⋅(2⋅(-1-r)))2⋅2
Factor 2 out of 2⋅2+2(-2⋅(2⋅(-1-r))).
y=-2±2(2-2⋅(2⋅(-1-r)))2⋅2
y=-2±2(2-2⋅(2⋅(-1-r)))2⋅2
Factor 2 out of 2-2⋅(2⋅(-1-r)).
Factor 2 out of 2.
y=-2±2(2(1)-2⋅(2⋅(-1-r)))2⋅2
Factor 2 out of -2⋅(2⋅(-1-r)).
y=-2±2(2(1)+2(-(2⋅(-1-r))))2⋅2
Factor 2 out of 2(1)+2(-(2⋅(-1-r))).
y=-2±2(2(1-(2⋅(-1-r))))2⋅2
y=-2±2(2(1-(2⋅(-1-r))))2⋅2
Apply the distributive property.
y=-2±2(2(1-(2⋅-1+2(-r))))2⋅2
Multiply 2 by -1.
y=-2±2(2(1-(-2+2(-r))))2⋅2
Multiply -1 by 2.
y=-2±2(2(1-(-2-2r)))2⋅2
Apply the distributive property.
y=-2±2(2(1+2-(-2r)))2⋅2
Multiply -1 by -2.
y=-2±2(2(1+2-(-2r)))2⋅2
Multiply -2 by -1.
y=-2±2(2(1+2+2r))2⋅2
Add 1 and 2.
y=-2±2⋅(2(3+2r))2⋅2
Multiply 2 by 2.
y=-2±4(3+2r)2⋅2
Rewrite 4 as 22.
y=-2±22(3+2r)2⋅2
Pull terms out from under the radical.
y=-2±23+2r2⋅2
y=-2±23+2r2⋅2
Multiply 2 by 2.
y=-2±23+2r4
Simplify -2±23+2r4.
y=-1±3+2r2
y=-1±3+2r2
The final answer is the combination of both solutions.
y=-1-3+2r2
y=-1+2r+32
Solve for y r=2y^2+2y-1

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