6n^2+7n=20

Solution for 6n^2+7n=20 equation:

Simplifying
6n2 + 7n = 20

Reorder the terms:
7n + 6n2 = 20

Solving
7n + 6n2 = 20

Solving for variable 'n'.

Reorder the terms:
-20 + 7n + 6n2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 7n + 6n2 = 0

Factor a trinomial.
(-5 + -2n)(4 + -3n) = 0

Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 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 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

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

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

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {-2.5, 1.333333333}