12n(n-4)-5n=10n-3n

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Solution for 12n(n-4)-5n=10n-3n equation:


Simplifying
12n(n + -4) + -5n = 10n + -3n

Reorder the terms:
12n(-4 + n) + -5n = 10n + -3n
(-4 * 12n + n * 12n) + -5n = 10n + -3n
(-48n + 12n2) + -5n = 10n + -3n

Reorder the terms:
-48n + -5n + 12n2 = 10n + -3n

Combine like terms: -48n + -5n = -53n
-53n + 12n2 = 10n + -3n

Combine like terms: 10n + -3n = 7n
-53n + 12n2 = 7n

Solving
-53n + 12n2 = 7n

Solving for variable 'n'.

Reorder the terms:
-53n + -7n + 12n2 = 7n + -7n

Combine like terms: -53n + -7n = -60n
-60n + 12n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-60n + 12n2 = 0

Factor out the Greatest Common Factor (GCF), '12n'.
12n(-5 + 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 '(-5 + n)' equal to zero and attempt to solve: Simplifying -5 + n = 0 Solving -5 + n = 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 + n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + n = 0 + 5 n = 0 + 5 Combine like terms: 0 + 5 = 5 n = 5 Simplifying n = 5

Solution

n = {0, 5}

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