(y-6)(y-6)=y-4

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Solution for (y-6)(y-6)=y-4 equation: 


Simplifying
(y + -6)(y + -6) = y + -4

Reorder the terms:
(-6 + y)(y + -6) = y + -4

Reorder the terms:
(-6 + y)(-6 + y) = y + -4

Multiply (-6 + y) * (-6 + y)
(-6(-6 + y) + y(-6 + y)) = y + -4
((-6 * -6 + y * -6) + y(-6 + y)) = y + -4
((36 + -6y) + y(-6 + y)) = y + -4
(36 + -6y + (-6 * y + y * y)) = y + -4
(36 + -6y + (-6y + y2)) = y + -4

Combine like terms: -6y + -6y = -12y
(36 + -12y + y2) = y + -4

Reorder the terms:
36 + -12y + y2 = -4 + y

Solving
36 + -12y + y2 = -4 + y

Solving for variable 'y'.

Reorder the terms:
36 + 4 + -12y + -1y + y2 = -4 + y + 4 + -1y

Combine like terms: 36 + 4 = 40
40 + -12y + -1y + y2 = -4 + y + 4 + -1y

Combine like terms: -12y + -1y = -13y
40 + -13y + y2 = -4 + y + 4 + -1y

Reorder the terms:
40 + -13y + y2 = -4 + 4 + y + -1y

Combine like terms: -4 + 4 = 0
40 + -13y + y2 = 0 + y + -1y
40 + -13y + y2 = y + -1y

Combine like terms: y + -1y = 0
40 + -13y + y2 = 0

Factor a trinomial.
(5 + -1y)(8 + -1y) = 0


Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

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 = {5, 8}

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