2n^2(n+6)(n-3)=0

Solution for 2n^2(n+6)(n-3)=0 equation:

Simplifying
2n2(n + 6)(n + -3) = 0

Reorder the terms:
2n2(6 + n)(n + -3) = 0

Reorder the terms:
2n2(6 + n)(-3 + n) = 0

Multiply (6 + n) * (-3 + n)
2n2(6(-3 + n) + n(-3 + n)) = 0
2n2((-3 * 6 + n * 6) + n(-3 + n)) = 0
2n2((-18 + 6n) + n(-3 + n)) = 0
2n2(-18 + 6n + (-3 * n + n * n)) = 0
2n2(-18 + 6n + (-3n + n2)) = 0

Combine like terms: 6n + -3n = 3n
2n2(-18 + 3n + n2) = 0
(-18 * 2n2 + 3n * 2n2 + n2 * 2n2) = 0
(-36n2 + 6n3 + 2n4) = 0

Solving
-36n2 + 6n3 + 2n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n2'.
2n2(-18 + 3n + n2) = 0

Factor a trinomial.
2n2((-6 + -1n)(3 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}
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
Subproblem 3
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
Solution
n = {0, -6, 3}