207n^2-12n-6=-3n^2

Solution for 207n^2-12n-6=-3n^2 equation:

Simplifying
207n2 + -12n + -6 = -3n2

Reorder the terms:
-6 + -12n + 207n2 = -3n2

Solving
-6 + -12n + 207n2 = -3n2

Solving for variable 'n'.

Combine like terms: 207n2 + 3n2 = 210n2
-6 + -12n + 210n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-6 + -12n + 210n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -2n + 35n2) = 0

Factor a trinomial.
6((-1 + -7n)(1 + -5n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -7n)' equal to zero and attempt to solve:

Simplifying
-1 + -7n = 0

Solving
-1 + -7n = 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 + -7n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7n = 0 + 1
-7n = 0 + 1

Combine like terms: 0 + 1 = 1
-7n = 1

Divide each side by '-7'.
n = -0.1428571429

Simplifying
n = -0.1428571429
Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve:

Simplifying
1 + -5n = 0

Solving
1 + -5n = 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 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-0.1428571429, 0.2}