7n(n)+12n-175=-7-2n

Solution for 7n(n)+12n-175=-7-2n equation:

Simplifying
7n(n) + 12n + -175 = -7 + -2n

Multiply n * n
7n2 + 12n + -175 = -7 + -2n

Reorder the terms:
-175 + 12n + 7n2 = -7 + -2n

Solving
-175 + 12n + 7n2 = -7 + -2n

Solving for variable 'n'.

Reorder the terms:
-175 + 7 + 12n + 2n + 7n2 = -7 + -2n + 7 + 2n

Combine like terms: -175 + 7 = -168
-168 + 12n + 2n + 7n2 = -7 + -2n + 7 + 2n

Combine like terms: 12n + 2n = 14n
-168 + 14n + 7n2 = -7 + -2n + 7 + 2n

Reorder the terms:
-168 + 14n + 7n2 = -7 + 7 + -2n + 2n

Combine like terms: -7 + 7 = 0
-168 + 14n + 7n2 = 0 + -2n + 2n
-168 + 14n + 7n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-168 + 14n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-24 + 2n + n2) = 0

Factor a trinomial.
7((-6 + -1n)(4 + -1n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-6, 4}