7n^2=42+35n

Solution for 7n^2=42+35n equation:

Simplifying
7n2 = 42 + 35n

Solving
7n2 = 42 + 35n

Solving for variable 'n'.

Reorder the terms:
-42 + -35n + 7n2 = 42 + 35n + -42 + -35n

Reorder the terms:
-42 + -35n + 7n2 = 42 + -42 + 35n + -35n

Combine like terms: 42 + -42 = 0
-42 + -35n + 7n2 = 0 + 35n + -35n
-42 + -35n + 7n2 = 35n + -35n

Combine like terms: 35n + -35n = 0
-42 + -35n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -5n + n2) = 0

Factor a trinomial.
7((-1 + -1n)(6 + -1n)) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-1, 6}