12n(n+3)=7n-15

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Solution for 12n(n+3)=7n-15 equation: 


Simplifying
12n(n + 3) = 7n + -15

Reorder the terms:
12n(3 + n) = 7n + -15
(3 * 12n + n * 12n) = 7n + -15
(36n + 12n2) = 7n + -15

Reorder the terms:
36n + 12n2 = -15 + 7n

Solving
36n + 12n2 = -15 + 7n

Solving for variable 'n'.

Reorder the terms:
15 + 36n + -7n + 12n2 = -15 + 7n + 15 + -7n

Combine like terms: 36n + -7n = 29n
15 + 29n + 12n2 = -15 + 7n + 15 + -7n

Reorder the terms:
15 + 29n + 12n2 = -15 + 15 + 7n + -7n

Combine like terms: -15 + 15 = 0
15 + 29n + 12n2 = 0 + 7n + -7n
15 + 29n + 12n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
15 + 29n + 12n2 = 0

Factor a trinomial.
(5 + 3n)(3 + 4n) = 0


Subproblem 1
Set the factor '(5 + 3n)' equal to zero and attempt to solve:

Simplifying
5 + 3n = 0

Solving
5 + 3n = 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 + 3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3n = 0 + -5
3n = 0 + -5

Combine like terms: 0 + -5 = -5
3n = -5

Divide each side by '3'.
n = -1.666666667

Simplifying
n = -1.666666667

Subproblem 2
Set the factor '(3 + 4n)' equal to zero and attempt to solve:

Simplifying
3 + 4n = 0

Solving
3 + 4n = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4n = 0 + -3
4n = 0 + -3

Combine like terms: 0 + -3 = -3
4n = -3

Divide each side by '4'.
n = -0.75

Simplifying
n = -0.75
Solution
n = {-1.666666667, -0.75}

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