3(n+11)-5n=-2n(n-12)+9

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Solution for 3(n+11)-5n=-2n(n-12)+9 equation: 


Simplifying
3(n + 11) + -5n = -2n(n + -12) + 9

Reorder the terms:
3(11 + n) + -5n = -2n(n + -12) + 9
(11 * 3 + n * 3) + -5n = -2n(n + -12) + 9
(33 + 3n) + -5n = -2n(n + -12) + 9

Combine like terms: 3n + -5n = -2n
33 + -2n = -2n(n + -12) + 9

Reorder the terms:
33 + -2n = -2n(-12 + n) + 9
33 + -2n = (-12 * -2n + n * -2n) + 9
33 + -2n = (24n + -2n2) + 9

Reorder the terms:
33 + -2n = 9 + 24n + -2n2

Solving
33 + -2n = 9 + 24n + -2n2

Solving for variable 'n'.

Reorder the terms:
33 + -9 + -2n + -24n + 2n2 = 9 + 24n + -2n2 + -9 + -24n + 2n2

Combine like terms: 33 + -9 = 24
24 + -2n + -24n + 2n2 = 9 + 24n + -2n2 + -9 + -24n + 2n2

Combine like terms: -2n + -24n = -26n
24 + -26n + 2n2 = 9 + 24n + -2n2 + -9 + -24n + 2n2

Reorder the terms:
24 + -26n + 2n2 = 9 + -9 + 24n + -24n + -2n2 + 2n2

Combine like terms: 9 + -9 = 0
24 + -26n + 2n2 = 0 + 24n + -24n + -2n2 + 2n2
24 + -26n + 2n2 = 24n + -24n + -2n2 + 2n2

Combine like terms: 24n + -24n = 0
24 + -26n + 2n2 = 0 + -2n2 + 2n2
24 + -26n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
24 + -26n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -13n + n2) = 0

Factor a trinomial.
2((1 + -1n)(12 + -1n)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1

Subproblem 2
Set the factor '(12 + -1n)' equal to zero and attempt to solve:

Simplifying
12 + -1n = 0

Solving
12 + -1n = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1n = 0 + -12
-1n = 0 + -12

Combine like terms: 0 + -12 = -12
-1n = -12

Divide each side by '-1'.
n = 12

Simplifying
n = 12
Solution
n = {1, 12}

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