7n^2=42-7n

Solution for 7n^2=42-7n equation:

Simplifying
7n2 = 42 + -7n

Solving
7n2 = 42 + -7n

Solving for variable 'n'.

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

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

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

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

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

Factor a trinomial.
7((-3 + -1n)(2 + -1n)) = 0

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-3, 2}