6(n^2+2n)=-7(n-1)

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Solution for 6(n^2+2n)=-7(n-1) equation: 


Simplifying
6(n2 + 2n) = -7(n + -1)

Reorder the terms:
6(2n + n2) = -7(n + -1)
(2n * 6 + n2 * 6) = -7(n + -1)
(12n + 6n2) = -7(n + -1)

Reorder the terms:
12n + 6n2 = -7(-1 + n)
12n + 6n2 = (-1 * -7 + n * -7)
12n + 6n2 = (7 + -7n)

Solving
12n + 6n2 = 7 + -7n

Solving for variable 'n'.

Reorder the terms:
-7 + 12n + 7n + 6n2 = 7 + -7n + -7 + 7n

Combine like terms: 12n + 7n = 19n
-7 + 19n + 6n2 = 7 + -7n + -7 + 7n

Reorder the terms:
-7 + 19n + 6n2 = 7 + -7 + -7n + 7n

Combine like terms: 7 + -7 = 0
-7 + 19n + 6n2 = 0 + -7n + 7n
-7 + 19n + 6n2 = -7n + 7n

Combine like terms: -7n + 7n = 0
-7 + 19n + 6n2 = 0

Factor a trinomial.
(-7 + -2n)(1 + -3n) = 0


Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve:

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5

Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-3.5, 0.3333333333}

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