2q^2-3q-27=0

Solution for 2q^2-3q-27=0 equation:

Simplifying
2q2 + -3q + -27 = 0

Reorder the terms:
-27 + -3q + 2q2 = 0

Solving
-27 + -3q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-3 + -1q)(9 + -2q) = 0

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 '(9 + -2q)' equal to zero and attempt to solve:

Simplifying
9 + -2q = 0

Solving
9 + -2q = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2q = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2q = 0 + -9
-2q = 0 + -9

Combine like terms: 0 + -9 = -9
-2q = -9

Divide each side by '-2'.
q = 4.5

Simplifying
q = 4.5
Solution
q = {-3, 4.5}