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

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

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

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

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

Multiply (-2 + 4n) * (6 + 5n)
(-2(6 + 5n) + 4n * (6 + 5n)) = 0
((6 * -2 + 5n * -2) + 4n * (6 + 5n)) = 0
((-12 + -10n) + 4n * (6 + 5n)) = 0
(-12 + -10n + (6 * 4n + 5n * 4n)) = 0
(-12 + -10n + (24n + 20n2)) = 0

Combine like terms: -10n + 24n = 14n
(-12 + 14n + 20n2) = 0

Solving
-12 + 14n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7n + 10n2) = 0

Factor a trinomial.
2((-6 + -5n)(1 + -2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -5n)' equal to zero and attempt to solve:

Simplifying
-6 + -5n = 0

Solving
-6 + -5n = 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 + -5n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -5n = 0 + 6
-5n = 0 + 6

Combine like terms: 0 + 6 = 6
-5n = 6

Divide each side by '-5'.
n = -1.2

Simplifying
n = -1.2
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 = {-1.2, 0.5}