7n^2+17n=-5n+24

Solution for 7n^2+17n=-5n+24 equation:

Simplifying
7n2 + 17n = -5n + 24

Reorder the terms:
17n + 7n2 = -5n + 24

Reorder the terms:
17n + 7n2 = 24 + -5n

Solving
17n + 7n2 = 24 + -5n

Solving for variable 'n'.

Reorder the terms:
-24 + 17n + 5n + 7n2 = 24 + -5n + -24 + 5n

Combine like terms: 17n + 5n = 22n
-24 + 22n + 7n2 = 24 + -5n + -24 + 5n

Reorder the terms:
-24 + 22n + 7n2 = 24 + -24 + -5n + 5n

Combine like terms: 24 + -24 = 0
-24 + 22n + 7n2 = 0 + -5n + 5n
-24 + 22n + 7n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
-24 + 22n + 7n2 = 0

Factor a trinomial.
(-4 + -1n)(6 + -7n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 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 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Solution
n = {-4, 0.8571428571}