2q^2+4q-6=0

Solution for 2q^2+4q-6=0 equation:

Simplifying
2q2 + 4q + -6 = 0

Reorder the terms:
-6 + 4q + 2q2 = 0

Solving
-6 + 4q + 2q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2q + q2) = 0

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

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

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Solution
q = {-3, 1}