7n^2+41n+58=-10n+4

Solution for 7n^2+41n+58=-10n+4 equation:

Simplifying
7n2 + 41n + 58 = -10n + 4

Reorder the terms:
58 + 41n + 7n2 = -10n + 4

Reorder the terms:
58 + 41n + 7n2 = 4 + -10n

Solving
58 + 41n + 7n2 = 4 + -10n

Solving for variable 'n'.

Reorder the terms:
58 + -4 + 41n + 10n + 7n2 = 4 + -10n + -4 + 10n

Combine like terms: 58 + -4 = 54
54 + 41n + 10n + 7n2 = 4 + -10n + -4 + 10n

Combine like terms: 41n + 10n = 51n
54 + 51n + 7n2 = 4 + -10n + -4 + 10n

Reorder the terms:
54 + 51n + 7n2 = 4 + -4 + -10n + 10n

Combine like terms: 4 + -4 = 0
54 + 51n + 7n2 = 0 + -10n + 10n
54 + 51n + 7n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
54 + 51n + 7n2 = 0

Factor a trinomial.
(6 + n)(9 + 7n) = 0

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

Simplifying
6 + n = 0

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

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(9 + 7n)' equal to zero and attempt to solve:

Simplifying
9 + 7n = 0

Solving
9 + 7n = 0

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

Add '-9' to each side of the equation.
9 + -9 + 7n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 7n = 0 + -9
7n = 0 + -9

Combine like terms: 0 + -9 = -9
7n = -9

Divide each side by '7'.
n = -1.285714286

Simplifying
n = -1.285714286
Solution
n = {-6, -1.285714286}