70n^2=30+8n

Solution for 70n^2=30+8n equation:

Simplifying
70n2 = 30 + 8n

Solving
70n2 = 30 + 8n

Solving for variable 'n'.

Reorder the terms:
-30 + -8n + 70n2 = 30 + 8n + -30 + -8n

Reorder the terms:
-30 + -8n + 70n2 = 30 + -30 + 8n + -8n

Combine like terms: 30 + -30 = 0
-30 + -8n + 70n2 = 0 + 8n + -8n
-30 + -8n + 70n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-30 + -8n + 70n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4n + 35n2) = 0

Factor a trinomial.
2((-3 + -5n)(5 + -7n)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve:

Simplifying
5 + -7n = 0

Solving
5 + -7n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7n = 0 + -5
-7n = 0 + -5

Combine like terms: 0 + -5 = -5
-7n = -5

Divide each side by '-7'.
n = 0.7142857143

Simplifying
n = 0.7142857143
Solution
n = {-0.6, 0.7142857143}