2n(4n+5)=-6(n-3)-8

Solution for 2n(4n+5)=-6(n-3)-8 equation:

Simplifying
2n(4n + 5) = -6(n + -3) + -8

Reorder the terms:
2n(5 + 4n) = -6(n + -3) + -8
(5 * 2n + 4n * 2n) = -6(n + -3) + -8
(10n + 8n2) = -6(n + -3) + -8

Reorder the terms:
10n + 8n2 = -6(-3 + n) + -8
10n + 8n2 = (-3 * -6 + n * -6) + -8
10n + 8n2 = (18 + -6n) + -8

Reorder the terms:
10n + 8n2 = 18 + -8 + -6n

Combine like terms: 18 + -8 = 10
10n + 8n2 = 10 + -6n

Solving
10n + 8n2 = 10 + -6n

Solving for variable 'n'.

Reorder the terms:
-10 + 10n + 6n + 8n2 = 10 + -6n + -10 + 6n

Combine like terms: 10n + 6n = 16n
-10 + 16n + 8n2 = 10 + -6n + -10 + 6n

Reorder the terms:
-10 + 16n + 8n2 = 10 + -10 + -6n + 6n

Combine like terms: 10 + -10 = 0
-10 + 16n + 8n2 = 0 + -6n + 6n
-10 + 16n + 8n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
-10 + 16n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 8n + 4n2) = 0

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

Ignore the factor 2.
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 + -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 = {-2.5, 0.5}