y(y-22)=3(7-6y)

Solution for y(y-22)=3(7-6y) equation:

Simplifying
y(y + -22) = 3(7 + -6y)

Reorder the terms:
y(-22 + y) = 3(7 + -6y)
(-22 * y + y * y) = 3(7 + -6y)
(-22y + y2) = 3(7 + -6y)
-22y + y2 = (7 * 3 + -6y * 3)
-22y + y2 = (21 + -18y)

Solving
-22y + y2 = 21 + -18y

Solving for variable 'y'.

Reorder the terms:
-21 + -22y + 18y + y2 = 21 + -18y + -21 + 18y

Combine like terms: -22y + 18y = -4y
-21 + -4y + y2 = 21 + -18y + -21 + 18y

Reorder the terms:
-21 + -4y + y2 = 21 + -21 + -18y + 18y

Combine like terms: 21 + -21 = 0
-21 + -4y + y2 = 0 + -18y + 18y
-21 + -4y + y2 = -18y + 18y

Combine like terms: -18y + 18y = 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}