7n^2-12=-40n

Solution for 7n^2-12=-40n equation:

Simplifying
7n2 + -12 = -40n

Reorder the terms:
-12 + 7n2 = -40n

Solving
-12 + 7n2 = -40n

Solving for variable 'n'.

Reorder the terms:
-12 + 40n + 7n2 = -40n + 40n

Combine like terms: -40n + 40n = 0
-12 + 40n + 7n2 = 0

Factor a trinomial.
(-6 + -1n)(2 + -7n) = 0

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 '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 0

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

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

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

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

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Solution
n = {-6, 0.2857142857}