3q^2-q-420=0

Solution for 3q^2-q-420=0 equation:

Simplifying
3q2 + -1q + -420 = 0

Reorder the terms:
-420 + -1q + 3q2 = 0

Solving
-420 + -1q + 3q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-35 + -3q)(12 + -1q) = 0

Subproblem 1
Set the factor '(-35 + -3q)' equal to zero and attempt to solve:

Simplifying
-35 + -3q = 0

Solving
-35 + -3q = 0

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

Add '35' to each side of the equation.
-35 + 35 + -3q = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -3q = 0 + 35
-3q = 0 + 35

Combine like terms: 0 + 35 = 35
-3q = 35

Divide each side by '-3'.
q = -11.66666667

Simplifying
q = -11.66666667
Subproblem 2
Set the factor '(12 + -1q)' equal to zero and attempt to solve:

Simplifying
12 + -1q = 0

Solving
12 + -1q = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1q = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1q = 0 + -12
-1q = 0 + -12

Combine like terms: 0 + -12 = -12
-1q = -12

Divide each side by '-1'.
q = 12

Simplifying
q = 12
Solution
q = {-11.66666667, 12}