Simplifying
q^{2} + 3q + -70 = 0
Reorder the terms:
-70 + 3q + q^{2} = 0
Solving
-70 + 3q + q^{2} = 0
Solving for variable 'q'.
Factor a trinomial.
(-10 + -1q)(7 + -1q) = 0
#### Subproblem 1

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
#### Subproblem 2

Set the factor '(7 + -1q)' equal to zero and attempt to solve:
Simplifying
7 + -1q = 0
Solving
7 + -1q = 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 + -1q = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -1q = 0 + -7
-1q = 0 + -7
Combine like terms: 0 + -7 = -7
-1q = -7
Divide each side by '-1'.
q = 7
Simplifying
q = 7#### Solution

q = {-10, 7}