42n^2+150n-300=0

Solution for 42n^2+150n-300=0 equation:

Simplifying
42n2 + 150n + -300 = 0

Reorder the terms:
-300 + 150n + 42n2 = 0

Solving
-300 + 150n + 42n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-50 + 25n + 7n2) = 0

Factor a trinomial.
6((-5 + -1n)(10 + -7n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-5 + -1n)' equal to zero and attempt to solve:

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(10 + -7n)' equal to zero and attempt to solve:

Simplifying
10 + -7n = 0

Solving
10 + -7n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -7n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7n = 0 + -10
-7n = 0 + -10

Combine like terms: 0 + -10 = -10
-7n = -10

Divide each side by '-7'.
n = 1.428571429

Simplifying
n = 1.428571429
Solution
n = {-5, 1.428571429}