(y-2)(y-5)=7y-10

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Solution for (y-2)(y-5)=7y-10 equation: 


Simplifying
(y + -2)(y + -5) = 7y + -10

Reorder the terms:
(-2 + y)(y + -5) = 7y + -10

Reorder the terms:
(-2 + y)(-5 + y) = 7y + -10

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

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

Reorder the terms:
10 + -7y + y2 = -10 + 7y

Solving
10 + -7y + y2 = -10 + 7y

Solving for variable 'y'.

Reorder the terms:
10 + 10 + -7y + -7y + y2 = -10 + 7y + 10 + -7y

Combine like terms: 10 + 10 = 20
20 + -7y + -7y + y2 = -10 + 7y + 10 + -7y

Combine like terms: -7y + -7y = -14y
20 + -14y + y2 = -10 + 7y + 10 + -7y

Reorder the terms:
20 + -14y + y2 = -10 + 10 + 7y + -7y

Combine like terms: -10 + 10 = 0
20 + -14y + y2 = 0 + 7y + -7y
20 + -14y + y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
20 + -14y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -14y + -20 + y2 = 0 + -20

Reorder the terms:
20 + -20 + -14y + y2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -14y + y2 = 0 + -20
-14y + y2 = 0 + -20

Combine like terms: 0 + -20 = -20
-14y + y2 = -20

The y term is -14y.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14y + 49 + y2 = -20 + 49

Reorder the terms:
49 + -14y + y2 = -20 + 49

Combine like terms: -20 + 49 = 29
49 + -14y + y2 = 29

Factor a perfect square on the left side:
(y + -7)(y + -7) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(y + -7) equal to 5.385164807 and -5.385164807.


Subproblem 1
y + -7 = 5.385164807

Simplifying
y + -7 = 5.385164807

Reorder the terms:
-7 + y = 5.385164807

Solving
-7 + y = 5.385164807

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + y = 5.385164807 + 7

Combine like terms: -7 + 7 = 0
0 + y = 5.385164807 + 7
y = 5.385164807 + 7

Combine like terms: 5.385164807 + 7 = 12.385164807
y = 12.385164807

Simplifying
y = 12.385164807


Subproblem 2
y + -7 = -5.385164807

Simplifying
y + -7 = -5.385164807

Reorder the terms:
-7 + y = -5.385164807

Solving
-7 + y = -5.385164807

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + y = -5.385164807 + 7

Combine like terms: -7 + 7 = 0
0 + y = -5.385164807 + 7
y = -5.385164807 + 7

Combine like terms: -5.385164807 + 7 = 1.614835193
y = 1.614835193

Simplifying
y = 1.614835193


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.385164807, 1.614835193}

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