Simplifying
q2 + 3q + -70 = 0

Reorder the terms:
-70 + 3q + q2 = 0

Solving
-70 + 3q + q2 = 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}