5n^2+19n+90.25=156.25

Solution for 5n^2+19n+90.25=156.25 equation:

Simplifying
5n2 + 19n + 90.25 = 156.25

Reorder the terms:
90.25 + 19n + 5n2 = 156.25

Solving
90.25 + 19n + 5n2 = 156.25

Solving for variable 'n'.

Reorder the terms:
90.25 + -156.25 + 19n + 5n2 = 156.25 + -156.25

Combine like terms: 90.25 + -156.25 = -66
-66 + 19n + 5n2 = 156.25 + -156.25

Combine like terms: 156.25 + -156.25 = 0.00
-66 + 19n + 5n2 = 0.00

Factor a trinomial.
(-6 + -1n)(11 + -5n) = 0.00

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

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

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

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

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(11 + -5n)' equal to zero and attempt to solve:

Simplifying
11 + -5n = 0

Solving
11 + -5n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -5n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -5n = 0 + -11
-5n = 0 + -11

Combine like terms: 0 + -11 = -11
-5n = -11

Divide each side by '-5'.
n = 2.2

Simplifying
n = 2.2
Solution
n = {-6, 2.2}