(y-2)(y+5)=(2y-1)(y+1)+7

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Solution for (y-2)(y+5)=(2y-1)(y+1)+7 equation: 


Simplifying
(y + -2)(y + 5) = (2y + -1)(y + 1) + 7

Reorder the terms:
(-2 + y)(y + 5) = (2y + -1)(y + 1) + 7

Reorder the terms:
(-2 + y)(5 + y) = (2y + -1)(y + 1) + 7

Multiply (-2 + y) * (5 + y)
(-2(5 + y) + y(5 + y)) = (2y + -1)(y + 1) + 7
((5 * -2 + y * -2) + y(5 + y)) = (2y + -1)(y + 1) + 7
((-10 + -2y) + y(5 + y)) = (2y + -1)(y + 1) + 7
(-10 + -2y + (5 * y + y * y)) = (2y + -1)(y + 1) + 7
(-10 + -2y + (5y + y2)) = (2y + -1)(y + 1) + 7

Combine like terms: -2y + 5y = 3y
(-10 + 3y + y2) = (2y + -1)(y + 1) + 7

Reorder the terms:
-10 + 3y + y2 = (-1 + 2y)(y + 1) + 7

Reorder the terms:
-10 + 3y + y2 = (-1 + 2y)(1 + y) + 7

Multiply (-1 + 2y) * (1 + y)
-10 + 3y + y2 = (-1(1 + y) + 2y * (1 + y)) + 7
-10 + 3y + y2 = ((1 * -1 + y * -1) + 2y * (1 + y)) + 7
-10 + 3y + y2 = ((-1 + -1y) + 2y * (1 + y)) + 7
-10 + 3y + y2 = (-1 + -1y + (1 * 2y + y * 2y)) + 7
-10 + 3y + y2 = (-1 + -1y + (2y + 2y2)) + 7

Combine like terms: -1y + 2y = 1y
-10 + 3y + y2 = (-1 + 1y + 2y2) + 7

Reorder the terms:
-10 + 3y + y2 = -1 + 7 + 1y + 2y2

Combine like terms: -1 + 7 = 6
-10 + 3y + y2 = 6 + 1y + 2y2

Solving
-10 + 3y + y2 = 6 + 1y + 2y2

Solving for variable 'y'.

Reorder the terms:
-10 + -6 + 3y + -1y + y2 + -2y2 = 6 + 1y + 2y2 + -6 + -1y + -2y2

Combine like terms: -10 + -6 = -16
-16 + 3y + -1y + y2 + -2y2 = 6 + 1y + 2y2 + -6 + -1y + -2y2

Combine like terms: 3y + -1y = 2y
-16 + 2y + y2 + -2y2 = 6 + 1y + 2y2 + -6 + -1y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-16 + 2y + -1y2 = 6 + 1y + 2y2 + -6 + -1y + -2y2

Reorder the terms:
-16 + 2y + -1y2 = 6 + -6 + 1y + -1y + 2y2 + -2y2

Combine like terms: 6 + -6 = 0
-16 + 2y + -1y2 = 0 + 1y + -1y + 2y2 + -2y2
-16 + 2y + -1y2 = 1y + -1y + 2y2 + -2y2

Combine like terms: 1y + -1y = 0
-16 + 2y + -1y2 = 0 + 2y2 + -2y2
-16 + 2y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-16 + 2y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16 + -2y + y2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -2y + -16 + y2 = 0 + -16

Reorder the terms:
16 + -16 + -2y + y2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -2y + y2 = 0 + -16
-2y + y2 = 0 + -16

Combine like terms: 0 + -16 = -16
-2y + y2 = -16

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = -16 + 1

Reorder the terms:
1 + -2y + y2 = -16 + 1

Combine like terms: -16 + 1 = -15
1 + -2y + y2 = -15

Factor a perfect square on the left side:
(y + -1)(y + -1) = -15

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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