-4n(2n-5)=8n-20

Solution for -4n(2n-5)=8n-20 equation:

Simplifying
-4n(2n + -5) = 8n + -20

Reorder the terms:
-4n(-5 + 2n) = 8n + -20
(-5 * -4n + 2n * -4n) = 8n + -20
(20n + -8n2) = 8n + -20

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

Solving
20n + -8n2 = -20 + 8n

Solving for variable 'n'.

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

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

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

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

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

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

Factor a trinomial.
4((5 + -2n)(1 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {2.5, -1}