(2y*2y)-23y+67=(y-7)(y-7)

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Solution for (2y*2y)-23y+67=(y-7)(y-7) equation: 


Simplifying
(2y * 2y) + -23y + 67 = (y + -7)(y + -7)

Reorder the terms for easier multiplication:
(2 * 2y * y) + -23y + 67 = (y + -7)(y + -7)

Multiply 2 * 2
(4y * y) + -23y + 67 = (y + -7)(y + -7)

Multiply y * y
(4y2) + -23y + 67 = (y + -7)(y + -7)

Reorder the terms:
67 + -23y + (4y2) = (y + -7)(y + -7)

Reorder the terms:
67 + -23y + (4y2) = (-7 + y)(y + -7)

Reorder the terms:
67 + -23y + (4y2) = (-7 + y)(-7 + y)

Multiply (-7 + y) * (-7 + y)
67 + -23y + (4y2) = (-7(-7 + y) + y(-7 + y))
67 + -23y + (4y2) = ((-7 * -7 + y * -7) + y(-7 + y))
67 + -23y + (4y2) = ((49 + -7y) + y(-7 + y))
67 + -23y + (4y2) = (49 + -7y + (-7 * y + y * y))
67 + -23y + (4y2) = (49 + -7y + (-7y + y2))

Combine like terms: -7y + -7y = -14y
67 + -23y + (4y2) = (49 + -14y + y2)

Solving
67 + -23y + (4y2) = 49 + -14y + y2

Solving for variable 'y'.

Reorder the terms:
67 + -49 + -23y + 14y + (4y2) + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 67 + -49 = 18
18 + -23y + 14y + (4y2) + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: -23y + 14y = -9y
18 + -9y + (4y2) + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: (4y2) + -1y2 = 3y2
18 + -9y + 3y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Reorder the terms:
18 + -9y + 3y2 = 49 + -49 + -14y + 14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
18 + -9y + 3y2 = 0 + -14y + 14y + y2 + -1y2
18 + -9y + 3y2 = -14y + 14y + y2 + -1y2

Combine like terms: -14y + 14y = 0
18 + -9y + 3y2 = 0 + y2 + -1y2
18 + -9y + 3y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
18 + -9y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -3y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + -3y + y2)' equal to zero and attempt to solve:

Simplifying
6 + -3y + y2 = 0

Solving
6 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -3y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + -3y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -3y + y2 = 0 + -6
-3y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
-3y + y2 = -6

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -6 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -6 + 2.25

Combine like terms: -6 + 2.25 = -3.75
2.25 + -3y + y2 = -3.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = -3.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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