35n^2+24=-61n

Solution for 35n^2+24=-61n equation:

Simplifying
35n2 + 24 = -61n

Reorder the terms:
24 + 35n2 = -61n

Solving
24 + 35n2 = -61n

Solving for variable 'n'.

Reorder the terms:
24 + 61n + 35n2 = -61n + 61n

Combine like terms: -61n + 61n = 0
24 + 61n + 35n2 = 0

Factor a trinomial.
(8 + 7n)(3 + 5n) = 0

Subproblem 1
Set the factor '(8 + 7n)' equal to zero and attempt to solve:

Simplifying
8 + 7n = 0

Solving
8 + 7n = 0

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

Add '-8' to each side of the equation.
8 + -8 + 7n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7n = 0 + -8
7n = 0 + -8

Combine like terms: 0 + -8 = -8
7n = -8

Divide each side by '7'.
n = -1.142857143

Simplifying
n = -1.142857143
Subproblem 2
Set the factor '(3 + 5n)' equal to zero and attempt to solve:

Simplifying
3 + 5n = 0

Solving
3 + 5n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5n = 0 + -3
5n = 0 + -3

Combine like terms: 0 + -3 = -3
5n = -3

Divide each side by '5'.
n = -0.6

Simplifying
n = -0.6
Solution
n = {-1.142857143, -0.6}