(y-5)(y-5)=16

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Solution for (y-5)(y-5)=16 equation: 


Simplifying
(y + -5)(y + -5) = 16

Reorder the terms:
(-5 + y)(y + -5) = 16

Reorder the terms:
(-5 + y)(-5 + y) = 16

Multiply (-5 + y) * (-5 + y)
(-5(-5 + y) + y(-5 + y)) = 16
((-5 * -5 + y * -5) + y(-5 + y)) = 16
((25 + -5y) + y(-5 + y)) = 16
(25 + -5y + (-5 * y + y * y)) = 16
(25 + -5y + (-5y + y2)) = 16

Combine like terms: -5y + -5y = -10y
(25 + -10y + y2) = 16

Solving
25 + -10y + y2 = 16

Solving for variable 'y'.

Reorder the terms:
25 + -16 + -10y + y2 = 16 + -16

Combine like terms: 25 + -16 = 9
9 + -10y + y2 = 16 + -16

Combine like terms: 16 + -16 = 0
9 + -10y + y2 = 0

Factor a trinomial.
(1 + -1y)(9 + -1y) = 0


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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

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

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

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

Simplifying
y = 1

Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {1, 9}

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