What is the answer to 2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2 ?

The answer to 2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2 is y=-1

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2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2

2 (y - 2) (y + 2) - (y - 5) (y + 3) = (y - 1)^{2} + 2

y = - 1

Solution steps

2 (y - 2) (y + 2) - (y - 5) (y + 3) = (y - 1)^{2} + 2

Expand

2 (y - 2) (y + 2) - (y - 5) (y + 3) : y^{2} + 2 y + 7

Expand

(y - 1)^{2} + 2 : y^{2} - 2 y + 3

y^{2} + 2 y + 7 = y^{2} - 2 y + 3

Move

7

to the right side

y^{2} + 2 y = y^{2} - 2 y - 4

Subtract

y^{2} - 2 y

from both sides

y^{2} + 2 y - (y^{2} - 2 y) = y^{2} - 2 y - 4 - (y^{2} - 2 y)

Simplify

4 y = - 4

Divide both sides by

4

y = - 1

3 (4 x - 7) = 27

5 x - 4 = 2 x + 8

\frac{2 t + 5}{6} + \frac{t - 4}{9} + \frac{3 t + 7}{2} = \frac{1}{3}

x, 4 x - 9 y = - 9

\frac{2 x}{5} - \frac{3}{2} = - 1 - \frac{x}{10}

What is the answer to 2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2 ?
The answer to 2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2 is y=-1
Solve for y: 2(y-2)(y+2)-(y-5)(y+3)=(y-1)^2+2
The solution is y=-1