12(10-n)+10n=8(n-12)-4

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Solution for 12(10-n)+10n=8(n-12)-4 equation: 


Simplifying
12(10 + -1n) + 10n = 8(n + -12) + -4
(10 * 12 + -1n * 12) + 10n = 8(n + -12) + -4
(120 + -12n) + 10n = 8(n + -12) + -4

Combine like terms: -12n + 10n = -2n
120 + -2n = 8(n + -12) + -4

Reorder the terms:
120 + -2n = 8(-12 + n) + -4
120 + -2n = (-12 * 8 + n * 8) + -4
120 + -2n = (-96 + 8n) + -4

Reorder the terms:
120 + -2n = -96 + -4 + 8n

Combine like terms: -96 + -4 = -100
120 + -2n = -100 + 8n

Solving
120 + -2n = -100 + 8n

Solving for variable 'n'.

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

Add '-8n' to each side of the equation.
120 + -2n + -8n = -100 + 8n + -8n

Combine like terms: -2n + -8n = -10n
120 + -10n = -100 + 8n + -8n

Combine like terms: 8n + -8n = 0
120 + -10n = -100 + 0
120 + -10n = -100

Add '-120' to each side of the equation.
120 + -120 + -10n = -100 + -120

Combine like terms: 120 + -120 = 0
0 + -10n = -100 + -120
-10n = -100 + -120

Combine like terms: -100 + -120 = -220
-10n = -220

Divide each side by '-10'.
n = 22

Simplifying
n = 22

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