-4n(2n-3)=12-8n

Solution for -4n(2n-3)=12-8n equation:

Simplifying
-4n(2n + -3) = 12 + -8n

Reorder the terms:
-4n(-3 + 2n) = 12 + -8n
(-3 * -4n + 2n * -4n) = 12 + -8n
(12n + -8n2) = 12 + -8n

Solving
12n + -8n2 = 12 + -8n

Solving for variable 'n'.

Reorder the terms:
-12 + 12n + 8n + -8n2 = 12 + -8n + -12 + 8n

Combine like terms: 12n + 8n = 20n
-12 + 20n + -8n2 = 12 + -8n + -12 + 8n

Reorder the terms:
-12 + 20n + -8n2 = 12 + -12 + -8n + 8n

Combine like terms: 12 + -12 = 0
-12 + 20n + -8n2 = 0 + -8n + 8n
-12 + 20n + -8n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-12 + 20n + -8n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 5n + -2n2) = 0

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

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

Simplifying
1 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {1.5, 1}