(y-2)(y-2)=25

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Solution for (y-2)(y-2)=25 equation: 


Simplifying
(y + -2)(y + -2) = 25

Reorder the terms:
(-2 + y)(y + -2) = 25

Reorder the terms:
(-2 + y)(-2 + y) = 25

Multiply (-2 + y) * (-2 + y)
(-2(-2 + y) + y(-2 + y)) = 25
((-2 * -2 + y * -2) + y(-2 + y)) = 25
((4 + -2y) + y(-2 + y)) = 25
(4 + -2y + (-2 * y + y * y)) = 25
(4 + -2y + (-2y + y2)) = 25

Combine like terms: -2y + -2y = -4y
(4 + -4y + y2) = 25

Solving
4 + -4y + y2 = 25

Solving for variable 'y'.

Reorder the terms:
4 + -25 + -4y + y2 = 25 + -25

Combine like terms: 4 + -25 = -21
-21 + -4y + y2 = 25 + -25

Combine like terms: 25 + -25 = 0
-21 + -4y + y2 = 0

Factor a trinomial.
(-3 + -1y)(7 + -1y) = 0


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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3

Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-3, 7}

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