2q^2+q-21=0

Solution for 2q^2+q-21=0 equation:

Simplifying
2q2 + q + -21 = 0

Reorder the terms:
-21 + q + 2q2 = 0

Solving
-21 + q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-7 + -2q)(3 + -1q) = 0

Subproblem 1
Set the factor '(-7 + -2q)' equal to zero and attempt to solve:

Simplifying
-7 + -2q = 0

Solving
-7 + -2q = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2q = 0 + 7
-2q = 0 + 7

Combine like terms: 0 + 7 = 7
-2q = 7

Divide each side by '-2'.
q = -3.5

Simplifying
q = -3.5
Subproblem 2
Set the factor '(3 + -1q)' equal to zero and attempt to solve:

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1q = 0 + -3
-1q = 0 + -3

Combine like terms: 0 + -3 = -3
-1q = -3

Divide each side by '-1'.
q = 3

Simplifying
q = 3
Solution
q = {-3.5, 3}