(y-7)(y-5)=3

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Solution for (y-7)(y-5)=3 equation: 


Simplifying
(y + -7)(y + -5) = 3

Reorder the terms:
(-7 + y)(y + -5) = 3

Reorder the terms:
(-7 + y)(-5 + y) = 3

Multiply (-7 + y) * (-5 + y)
(-7(-5 + y) + y(-5 + y)) = 3
((-5 * -7 + y * -7) + y(-5 + y)) = 3
((35 + -7y) + y(-5 + y)) = 3
(35 + -7y + (-5 * y + y * y)) = 3
(35 + -7y + (-5y + y2)) = 3

Combine like terms: -7y + -5y = -12y
(35 + -12y + y2) = 3

Solving
35 + -12y + y2 = 3

Solving for variable 'y'.

Reorder the terms:
35 + -3 + -12y + y2 = 3 + -3

Combine like terms: 35 + -3 = 32
32 + -12y + y2 = 3 + -3

Combine like terms: 3 + -3 = 0
32 + -12y + y2 = 0

Factor a trinomial.
(4 + -1y)(8 + -1y) = 0


Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

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 = {4, 8}

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