y^2+19y+90.25=12.25

Solution for y^2+19y+90.25=12.25 equation:

Simplifying
y2 + 19y + 90.25 = 12.25

Reorder the terms:
90.25 + 19y + y2 = 12.25

Solving
90.25 + 19y + y2 = 12.25

Solving for variable 'y'.

Reorder the terms:
90.25 + -12.25 + 19y + y2 = 12.25 + -12.25

Combine like terms: 90.25 + -12.25 = 78
78 + 19y + y2 = 12.25 + -12.25

Combine like terms: 12.25 + -12.25 = 0.00
78 + 19y + y2 = 0.00

Factor a trinomial.
(13 + y)(6 + y) = 0.00

Subproblem 1
Set the factor '(13 + y)' equal to zero and attempt to solve:

Simplifying
13 + y = 0

Solving
13 + y = 0

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

Add '-13' to each side of the equation.
13 + -13 + y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + y = 0 + -13
y = 0 + -13

Combine like terms: 0 + -13 = -13
y = -13

Simplifying
y = -13
Subproblem 2
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
Solution
y = {-13, -6}