(y-7)*(y-7)=(y+5)*(y+5)

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


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

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

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

Multiply (-7 + y) * (-7 + y)
(-7(-7 + y) + y(-7 + y)) = (y + 5)(y + 5)
((-7 * -7 + y * -7) + y(-7 + y)) = (y + 5)(y + 5)
((49 + -7y) + y(-7 + y)) = (y + 5)(y + 5)
(49 + -7y + (-7 * y + y * y)) = (y + 5)(y + 5)
(49 + -7y + (-7y + y2)) = (y + 5)(y + 5)

Combine like terms: -7y + -7y = -14y
(49 + -14y + y2) = (y + 5)(y + 5)

Reorder the terms:
49 + -14y + y2 = (5 + y)(y + 5)

Reorder the terms:
49 + -14y + y2 = (5 + y)(5 + y)

Multiply (5 + y) * (5 + y)
49 + -14y + y2 = (5(5 + y) + y(5 + y))
49 + -14y + y2 = ((5 * 5 + y * 5) + y(5 + y))
49 + -14y + y2 = ((25 + 5y) + y(5 + y))
49 + -14y + y2 = (25 + 5y + (5 * y + y * y))
49 + -14y + y2 = (25 + 5y + (5y + y2))

Combine like terms: 5y + 5y = 10y
49 + -14y + y2 = (25 + 10y + y2)

Add '-1y2' to each side of the equation.
49 + -14y + y2 + -1y2 = 25 + 10y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
49 + -14y + 0 = 25 + 10y + y2 + -1y2
49 + -14y = 25 + 10y + y2 + -1y2

Combine like terms: y2 + -1y2 = 0
49 + -14y = 25 + 10y + 0
49 + -14y = 25 + 10y

Solving
49 + -14y = 25 + 10y

Solving for variable 'y'.

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

Add '-10y' to each side of the equation.
49 + -14y + -10y = 25 + 10y + -10y

Combine like terms: -14y + -10y = -24y
49 + -24y = 25 + 10y + -10y

Combine like terms: 10y + -10y = 0
49 + -24y = 25 + 0
49 + -24y = 25

Add '-49' to each side of the equation.
49 + -49 + -24y = 25 + -49

Combine like terms: 49 + -49 = 0
0 + -24y = 25 + -49
-24y = 25 + -49

Combine like terms: 25 + -49 = -24
-24y = -24

Divide each side by '-24'.
y = 1

Simplifying
y = 1

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