y^2-2y+10=3y+4

Solution for y^2-2y+10=3y+4 equation:

Simplifying
y2 + -2y + 10 = 3y + 4

Reorder the terms:
10 + -2y + y2 = 3y + 4

Reorder the terms:
10 + -2y + y2 = 4 + 3y

Solving
10 + -2y + y2 = 4 + 3y

Solving for variable 'y'.

Reorder the terms:
10 + -4 + -2y + -3y + y2 = 4 + 3y + -4 + -3y

Combine like terms: 10 + -4 = 6
6 + -2y + -3y + y2 = 4 + 3y + -4 + -3y

Combine like terms: -2y + -3y = -5y
6 + -5y + y2 = 4 + 3y + -4 + -3y

Reorder the terms:
6 + -5y + y2 = 4 + -4 + 3y + -3y

Combine like terms: 4 + -4 = 0
6 + -5y + y2 = 0 + 3y + -3y
6 + -5y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
6 + -5y + y2 = 0

Factor a trinomial.
(2 + -1y)(3 + -1y) = 0

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Subproblem 2
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
Solution
y = {2, 3}