2y^2-13y+21=0

Solution for 2y^2-13y+21=0 equation:

Simplifying
2y2 + -13y + 21 = 0

Reorder the terms:
21 + -13y + 2y2 = 0

Solving
21 + -13y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -1y)(7 + -2y) = 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 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 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 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {3, 3.5}