4(5n-2)6n-6=

Solution for 4(5n-2)6n-6= equation:

Simplifying
4(5n + -2) * 6n + -6 = 0

Reorder the terms:
4(-2 + 5n) * 6n + -6 = 0

Reorder the terms for easier multiplication:
4 * 6n(-2 + 5n) + -6 = 0

Multiply 4 * 6
24n(-2 + 5n) + -6 = 0
(-2 * 24n + 5n * 24n) + -6 = 0
(-48n + 120n2) + -6 = 0

Reorder the terms:
-6 + -48n + 120n2 = 0

Solving
-6 + -48n + 120n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -8n + 20n2) = 0

Factor a trinomial.
6((-1 + -10n)(1 + -2n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -10n)' equal to zero and attempt to solve:

Simplifying
-1 + -10n = 0

Solving
-1 + -10n = 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 + -10n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -10n = 0 + 1
-10n = 0 + 1

Combine like terms: 0 + 1 = 1
-10n = 1

Divide each side by '-10'.
n = -0.1

Simplifying
n = -0.1
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

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

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

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

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {-0.1, 0.5}