=n(4n+6)

Solution for =n(4n+6) equation:

Simplifying
0 = n(4n + 6)

Reorder the terms:
0 = n(6 + 4n)
0 = (6 * n + 4n * n)
0 = (6n + 4n2)

Solving
0 = 6n + 4n2

Solving for variable 'n'.
Remove the zero:
-6n + -4n2 = 6n + 4n2 + -6n + -4n2

Reorder the terms:
-6n + -4n2 = 6n + -6n + 4n2 + -4n2

Combine like terms: 6n + -6n = 0
-6n + -4n2 = 0 + 4n2 + -4n2
-6n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
-6n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '-2n'.
-2n(3 + 2n) = 0

Ignore the factor -2.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Solution
n = {0, -1.5}