5y^2-32y+51=0

Solution for 5y^2-32y+51=0 equation:

Simplifying
5y2 + -32y + 51 = 0

Reorder the terms:
51 + -32y + 5y2 = 0

Solving
51 + -32y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -1y)(17 + -5y) = 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 '(17 + -5y)' equal to zero and attempt to solve:

Simplifying
17 + -5y = 0

Solving
17 + -5y = 0

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

Add '-17' to each side of the equation.
17 + -17 + -5y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -5y = 0 + -17
-5y = 0 + -17

Combine like terms: 0 + -17 = -17
-5y = -17

Divide each side by '-5'.
y = 3.4

Simplifying
y = 3.4
Solution
y = {3, 3.4}