20n^2+153n=5n-168

Solution for 20n^2+153n=5n-168 equation:

Simplifying
20n2 + 153n = 5n + -168

Reorder the terms:
153n + 20n2 = 5n + -168

Reorder the terms:
153n + 20n2 = -168 + 5n

Solving
153n + 20n2 = -168 + 5n

Solving for variable 'n'.

Reorder the terms:
168 + 153n + -5n + 20n2 = -168 + 5n + 168 + -5n

Combine like terms: 153n + -5n = 148n
168 + 148n + 20n2 = -168 + 5n + 168 + -5n

Reorder the terms:
168 + 148n + 20n2 = -168 + 168 + 5n + -5n

Combine like terms: -168 + 168 = 0
168 + 148n + 20n2 = 0 + 5n + -5n
168 + 148n + 20n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
168 + 148n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(42 + 37n + 5n2) = 0

Factor a trinomial.
4((6 + n)(7 + 5n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

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

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

Simplifying
n = -6
Subproblem 2
Set the factor '(7 + 5n)' equal to zero and attempt to solve:

Simplifying
7 + 5n = 0

Solving
7 + 5n = 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 + 5n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5n = 0 + -7
5n = 0 + -7

Combine like terms: 0 + -7 = -7
5n = -7

Divide each side by '5'.
n = -1.4

Simplifying
n = -1.4
Solution
n = {-6, -1.4}