y^2-5y+14=4y-6

Solution for y^2-5y+14=4y-6 equation:

Simplifying
y2 + -5y + 14 = 4y + -6

Reorder the terms:
14 + -5y + y2 = 4y + -6

Reorder the terms:
14 + -5y + y2 = -6 + 4y

Solving
14 + -5y + y2 = -6 + 4y

Solving for variable 'y'.

Reorder the terms:
14 + 6 + -5y + -4y + y2 = -6 + 4y + 6 + -4y

Combine like terms: 14 + 6 = 20
20 + -5y + -4y + y2 = -6 + 4y + 6 + -4y

Combine like terms: -5y + -4y = -9y
20 + -9y + y2 = -6 + 4y + 6 + -4y

Reorder the terms:
20 + -9y + y2 = -6 + 6 + 4y + -4y

Combine like terms: -6 + 6 = 0
20 + -9y + y2 = 0 + 4y + -4y
20 + -9y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
20 + -9y + y2 = 0

Factor a trinomial.
(4 + -1y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {4, 5}