(y-3)(y-3)-10(y-3)+25=0

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Solution for (y-3)(y-3)-10(y-3)+25=0 equation: 


Simplifying
(y + -3)(y + -3) + -10(y + -3) + 25 = 0

Reorder the terms:
(-3 + y)(y + -3) + -10(y + -3) + 25 = 0

Reorder the terms:
(-3 + y)(-3 + y) + -10(y + -3) + 25 = 0

Multiply (-3 + y) * (-3 + y)
(-3(-3 + y) + y(-3 + y)) + -10(y + -3) + 25 = 0
((-3 * -3 + y * -3) + y(-3 + y)) + -10(y + -3) + 25 = 0
((9 + -3y) + y(-3 + y)) + -10(y + -3) + 25 = 0
(9 + -3y + (-3 * y + y * y)) + -10(y + -3) + 25 = 0
(9 + -3y + (-3y + y2)) + -10(y + -3) + 25 = 0

Combine like terms: -3y + -3y = -6y
(9 + -6y + y2) + -10(y + -3) + 25 = 0

Reorder the terms:
9 + -6y + y2 + -10(-3 + y) + 25 = 0
9 + -6y + y2 + (-3 * -10 + y * -10) + 25 = 0
9 + -6y + y2 + (30 + -10y) + 25 = 0

Reorder the terms:
9 + 30 + 25 + -6y + -10y + y2 = 0

Combine like terms: 9 + 30 = 39
39 + 25 + -6y + -10y + y2 = 0

Combine like terms: 39 + 25 = 64
64 + -6y + -10y + y2 = 0

Combine like terms: -6y + -10y = -16y
64 + -16y + y2 = 0

Solving
64 + -16y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y)(8 + -1y) = 0


Subproblem 1
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {8, 8}

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