Y*Y+72=17Y

Solution for Y*Y+72=17Y equation:

Simplifying
Y * Y + 72 = 17Y

Multiply Y * Y
Y2 + 72 = 17Y

Reorder the terms:
72 + Y2 = 17Y

Solving
72 + Y2 = 17Y

Solving for variable 'Y'.

Reorder the terms:
72 + -17Y + Y2 = 17Y + -17Y

Combine like terms: 17Y + -17Y = 0
72 + -17Y + Y2 = 0

Factor a trinomial.
(8 + -1Y)(9 + -1Y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -1Y)' equal to zero and attempt to solve:

Simplifying
9 + -1Y = 0

Solving
9 + -1Y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1Y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1Y = 0 + -9
-1Y = 0 + -9

Combine like terms: 0 + -9 = -9
-1Y = -9

Divide each side by '-1'.
Y = 9

Simplifying
Y = 9
Solution
Y = {8, 9}