(6n-2)(4n+1)=

Solution for (6n-2)(4n+1)= equation:

Simplifying
(6n + -2)(4n + 1) = 0

Reorder the terms:
(-2 + 6n)(4n + 1) = 0

Reorder the terms:
(-2 + 6n)(1 + 4n) = 0

Multiply (-2 + 6n) * (1 + 4n)
(-2(1 + 4n) + 6n * (1 + 4n)) = 0
((1 * -2 + 4n * -2) + 6n * (1 + 4n)) = 0
((-2 + -8n) + 6n * (1 + 4n)) = 0
(-2 + -8n + (1 * 6n + 4n * 6n)) = 0
(-2 + -8n + (6n + 24n2)) = 0

Combine like terms: -8n + 6n = -2n
(-2 + -2n + 24n2) = 0

Solving
-2 + -2n + 24n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -1n + 12n2) = 0

Factor a trinomial.
2((-1 + -4n)(1 + -3n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 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 + -4n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-0.25, 0.3333333333}