y^2+7y+19=13

Solution for y^2+7y+19=13 equation:

Simplifying
y2 + 7y + 19 = 13

Reorder the terms:
19 + 7y + y2 = 13

Solving
19 + 7y + y2 = 13

Solving for variable 'y'.

Reorder the terms:
19 + -13 + 7y + y2 = 13 + -13

Combine like terms: 19 + -13 = 6
6 + 7y + y2 = 13 + -13

Combine like terms: 13 + -13 = 0
6 + 7y + y2 = 0

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

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

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 0

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

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

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

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

Simplifying
y = -1
Solution
y = {-6, -1}