-3n(6n+1)=18n+3

Solution for -3n(6n+1)=18n+3 equation:

Simplifying
-3n(6n + 1) = 18n + 3

Reorder the terms:
-3n(1 + 6n) = 18n + 3
(1 * -3n + 6n * -3n) = 18n + 3
(-3n + -18n2) = 18n + 3

Reorder the terms:
-3n + -18n2 = 3 + 18n

Solving
-3n + -18n2 = 3 + 18n

Solving for variable 'n'.

Reorder the terms:
-3 + -3n + -18n + -18n2 = 3 + 18n + -3 + -18n

Combine like terms: -3n + -18n = -21n
-3 + -21n + -18n2 = 3 + 18n + -3 + -18n

Reorder the terms:
-3 + -21n + -18n2 = 3 + -3 + 18n + -18n

Combine like terms: 3 + -3 = 0
-3 + -21n + -18n2 = 0 + 18n + -18n
-3 + -21n + -18n2 = 18n + -18n

Combine like terms: 18n + -18n = 0
-3 + -21n + -18n2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + 7n + 6n2) = 0

Factor a trinomial.
-3((1 + n)(1 + 6n)) = 0

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

Simplifying
1 + n = 0

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

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

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

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

Simplifying
1 + 6n = 0

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

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

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

Divide each side by '6'.
n = -0.1666666667

Simplifying
n = -0.1666666667
Solution
n = {-1, -0.1666666667}