8s(3n+1)=4(6n-2)

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Solution for 8s(3n+1)=4(6n-2) equation:


Simplifying
8s(3n + 1) = 4(6n + -2)

Reorder the terms:
8s(1 + 3n) = 4(6n + -2)
(1 * 8s + 3n * 8s) = 4(6n + -2)

Reorder the terms:
(24ns + 8s) = 4(6n + -2)
(24ns + 8s) = 4(6n + -2)

Reorder the terms:
24ns + 8s = 4(-2 + 6n)
24ns + 8s = (-2 * 4 + 6n * 4)
24ns + 8s = (-8 + 24n)

Solving
24ns + 8s = -8 + 24n

Solving for variable 'n'.

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

Add '-24n' to each side of the equation.
24ns + -24n + 8s = -8 + 24n + -24n

Reorder the terms:
-24n + 24ns + 8s = -8 + 24n + -24n

Combine like terms: 24n + -24n = 0
-24n + 24ns + 8s = -8 + 0
-24n + 24ns + 8s = -8

Add '-8s' to each side of the equation.
-24n + 24ns + 8s + -8s = -8 + -8s

Combine like terms: 8s + -8s = 0
-24n + 24ns + 0 = -8 + -8s
-24n + 24ns = -8 + -8s

Reorder the terms:
8 + -24n + 24ns + 8s = -8 + -8s + 8 + 8s

Reorder the terms:
8 + -24n + 24ns + 8s = -8 + 8 + -8s + 8s

Combine like terms: -8 + 8 = 0
8 + -24n + 24ns + 8s = 0 + -8s + 8s
8 + -24n + 24ns + 8s = -8s + 8s

Combine like terms: -8s + 8s = 0
8 + -24n + 24ns + 8s = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -3n + 3ns + s) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(1 + -3n + 3ns + s)' equal to zero and attempt to solve: Simplifying 1 + -3n + 3ns + s = 0 Solving 1 + -3n + 3ns + s = 0 Move all terms containing n to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -3n + 3ns + -1 + s = 0 + -1 Reorder the terms: 1 + -1 + -3n + 3ns + s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n + 3ns + s = 0 + -1 -3n + 3ns + s = 0 + -1 Combine like terms: 0 + -1 = -1 -3n + 3ns + s = -1 Add '-1s' to each side of the equation. -3n + 3ns + s + -1s = -1 + -1s Combine like terms: s + -1s = 0 -3n + 3ns + 0 = -1 + -1s -3n + 3ns = -1 + -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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