7n^2-67n-30=0

Solution for 7n^2-67n-30=0 equation:

Simplifying
7n2 + -67n + -30 = 0

Reorder the terms:
-30 + -67n + 7n2 = 0

Solving
-30 + -67n + 7n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -7n)(10 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -7n)' equal to zero and attempt to solve:

Simplifying
-3 + -7n = 0

Solving
-3 + -7n = 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 + -7n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7n = 0 + 3
-7n = 0 + 3

Combine like terms: 0 + 3 = 3
-7n = 3

Divide each side by '-7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {-0.4285714286, 10}