4q^2+2q-420=0

Solution for 4q^2+2q-420=0 equation:

Simplifying
4q2 + 2q + -420 = 0

Reorder the terms:
-420 + 2q + 4q2 = 0

Solving
-420 + 2q + 4q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-210 + q + 2q2) = 0

Factor a trinomial.
2((-21 + -2q)(10 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -2q)' equal to zero and attempt to solve:

Simplifying
-21 + -2q = 0

Solving
-21 + -2q = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2q = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2q = 0 + 21
-2q = 0 + 21

Combine like terms: 0 + 21 = 21
-2q = 21

Divide each side by '-2'.
q = -10.5

Simplifying
q = -10.5
Subproblem 2
Set the factor '(10 + -1q)' equal to zero and attempt to solve:

Simplifying
10 + -1q = 0

Solving
10 + -1q = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1q = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1q = 0 + -10
-1q = 0 + -10

Combine like terms: 0 + -10 = -10
-1q = -10

Divide each side by '-1'.
q = 10

Simplifying
q = 10
Solution
q = {-10.5, 10}