7n^2+8=30n

Solution for 7n^2+8=30n equation:

Simplifying
7n2 + 8 = 30n

Reorder the terms:
8 + 7n2 = 30n

Solving
8 + 7n2 = 30n

Solving for variable 'n'.

Reorder the terms:
8 + -30n + 7n2 = 30n + -30n

Combine like terms: 30n + -30n = 0
8 + -30n + 7n2 = 0

Factor a trinomial.
(2 + -7n)(4 + -1n) = 0

Subproblem 1
Set the factor '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -7n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Subproblem 2
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
Solution
n = {0.2857142857, 4}