y(y-7)=12(y-5)

Solution for y(y-7)=12(y-5) equation:

Simplifying
y(y + -7) = 12(y + -5)

Reorder the terms:
y(-7 + y) = 12(y + -5)
(-7 * y + y * y) = 12(y + -5)
(-7y + y2) = 12(y + -5)

Reorder the terms:
-7y + y2 = 12(-5 + y)
-7y + y2 = (-5 * 12 + y * 12)
-7y + y2 = (-60 + 12y)

Solving
-7y + y2 = -60 + 12y

Solving for variable 'y'.

Reorder the terms:
60 + -7y + -12y + y2 = -60 + 12y + 60 + -12y

Combine like terms: -7y + -12y = -19y
60 + -19y + y2 = -60 + 12y + 60 + -12y

Reorder the terms:
60 + -19y + y2 = -60 + 60 + 12y + -12y

Combine like terms: -60 + 60 = 0
60 + -19y + y2 = 0 + 12y + -12y
60 + -19y + y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
60 + -19y + y2 = 0

Factor a trinomial.
(4 + -1y)(15 + -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 '(15 + -1y)' equal to zero and attempt to solve:

Simplifying
15 + -1y = 0

Solving
15 + -1y = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1y = 0 + -15
-1y = 0 + -15

Combine like terms: 0 + -15 = -15
-1y = -15

Divide each side by '-1'.
y = 15

Simplifying
y = 15
Solution
y = {4, 15}