x+2y-19=-y^2+x+5

Solution for x+2y-19=-y^2+x+5 equation:

Simplifying
x + 2y + -19 = -1y2 + x + 5

Reorder the terms:
-19 + x + 2y = -1y2 + x + 5

Reorder the terms:
-19 + x + 2y = 5 + x + -1y2

Add '-1x' to each side of the equation.
-19 + x + -1x + 2y = 5 + x + -1x + -1y2

Combine like terms: x + -1x = 0
-19 + 0 + 2y = 5 + x + -1x + -1y2
-19 + 2y = 5 + x + -1x + -1y2

Combine like terms: x + -1x = 0
-19 + 2y = 5 + 0 + -1y2
-19 + 2y = 5 + -1y2

Solving
-19 + 2y = 5 + -1y2

Solving for variable 'y'.

Reorder the terms:
-19 + -5 + 2y + y2 = 5 + -1y2 + -5 + y2

Combine like terms: -19 + -5 = -24
-24 + 2y + y2 = 5 + -1y2 + -5 + y2

Reorder the terms:
-24 + 2y + y2 = 5 + -5 + -1y2 + y2

Combine like terms: 5 + -5 = 0
-24 + 2y + y2 = 0 + -1y2 + y2
-24 + 2y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-24 + 2y + y2 = 0

Factor a trinomial.
(-6 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
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
Solution
y = {-6, 4}