(y-7)(y-7)+y^2=(y+7)(y+7)

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


Simplifying
(y + -7)(y + -7) + y2 = (y + 7)(y + 7)

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

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

Multiply (-7 + y) * (-7 + y)
(-7(-7 + y) + y(-7 + y)) + y2 = (y + 7)(y + 7)
((-7 * -7 + y * -7) + y(-7 + y)) + y2 = (y + 7)(y + 7)
((49 + -7y) + y(-7 + y)) + y2 = (y + 7)(y + 7)
(49 + -7y + (-7 * y + y * y)) + y2 = (y + 7)(y + 7)
(49 + -7y + (-7y + y2)) + y2 = (y + 7)(y + 7)

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

Combine like terms: y2 + y2 = 2y2
49 + -14y + 2y2 = (y + 7)(y + 7)

Reorder the terms:
49 + -14y + 2y2 = (7 + y)(y + 7)

Reorder the terms:
49 + -14y + 2y2 = (7 + y)(7 + y)

Multiply (7 + y) * (7 + y)
49 + -14y + 2y2 = (7(7 + y) + y(7 + y))
49 + -14y + 2y2 = ((7 * 7 + y * 7) + y(7 + y))
49 + -14y + 2y2 = ((49 + 7y) + y(7 + y))
49 + -14y + 2y2 = (49 + 7y + (7 * y + y * y))
49 + -14y + 2y2 = (49 + 7y + (7y + y2))

Combine like terms: 7y + 7y = 14y
49 + -14y + 2y2 = (49 + 14y + y2)

Add '-49' to each side of the equation.
49 + -14y + -49 + 2y2 = 49 + 14y + -49 + y2

Reorder the terms:
49 + -49 + -14y + 2y2 = 49 + 14y + -49 + y2

Combine like terms: 49 + -49 = 0
0 + -14y + 2y2 = 49 + 14y + -49 + y2
-14y + 2y2 = 49 + 14y + -49 + y2

Reorder the terms:
-14y + 2y2 = 49 + -49 + 14y + y2

Combine like terms: 49 + -49 = 0
-14y + 2y2 = 0 + 14y + y2
-14y + 2y2 = 14y + y2

Solving
-14y + 2y2 = 14y + y2

Solving for variable 'y'.

Reorder the terms:
-14y + -14y + 2y2 + -1y2 = 14y + y2 + -14y + -1y2

Combine like terms: -14y + -14y = -28y
-28y + 2y2 + -1y2 = 14y + y2 + -14y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-28y + 1y2 = 14y + y2 + -14y + -1y2

Reorder the terms:
-28y + 1y2 = 14y + -14y + y2 + -1y2

Combine like terms: 14y + -14y = 0
-28y + 1y2 = 0 + y2 + -1y2
-28y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-28y + 1y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-28 + y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(-28 + y)' equal to zero and attempt to solve:

Simplifying
-28 + y = 0

Solving
-28 + y = 0

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

Add '28' to each side of the equation.
-28 + 28 + y = 0 + 28

Combine like terms: -28 + 28 = 0
0 + y = 0 + 28
y = 0 + 28

Combine like terms: 0 + 28 = 28
y = 28

Simplifying
y = 28
Solution
y = {0, 28}

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