-12n-4(1-3)=-12n(n+5)+8

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Solution for -12n-4(1-3)=-12n(n+5)+8 equation: 


Simplifying
-12n + -4(1 + -3) = -12n(n + 5) + 8

Combine like terms: 1 + -3 = -2
-12n + -4(-2) = -12n(n + 5) + 8

Multiply -4 * -2
-12n + 8 = -12n(n + 5) + 8

Reorder the terms:
8 + -12n = -12n(n + 5) + 8

Reorder the terms:
8 + -12n = -12n(5 + n) + 8
8 + -12n = (5 * -12n + n * -12n) + 8
8 + -12n = (-60n + -12n2) + 8

Reorder the terms:
8 + -12n = 8 + -60n + -12n2

Add '-8' to each side of the equation.
8 + -8 + -12n = 8 + -60n + -8 + -12n2

Combine like terms: 8 + -8 = 0
0 + -12n = 8 + -60n + -8 + -12n2
-12n = 8 + -60n + -8 + -12n2

Reorder the terms:
-12n = 8 + -8 + -60n + -12n2

Combine like terms: 8 + -8 = 0
-12n = 0 + -60n + -12n2
-12n = -60n + -12n2

Solving
-12n = -60n + -12n2

Solving for variable 'n'.

Combine like terms: -12n + 60n = 48n
48n + 12n2 = -60n + -12n2 + 60n + 12n2

Reorder the terms:
48n + 12n2 = -60n + 60n + -12n2 + 12n2

Combine like terms: -60n + 60n = 0
48n + 12n2 = 0 + -12n2 + 12n2
48n + 12n2 = -12n2 + 12n2

Combine like terms: -12n2 + 12n2 = 0
48n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '12n'.
12n(4 + n) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

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

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Solution
n = {0, -4}

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