2q^2+27q-14=0

Solution for 2q^2+27q-14=0 equation:

Simplifying
2q2 + 27q + -14 = 0

Reorder the terms:
-14 + 27q + 2q2 = 0

Solving
-14 + 27q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-14 + -1q)(1 + -2q) = 0

Subproblem 1
Set the factor '(-14 + -1q)' equal to zero and attempt to solve:

Simplifying
-14 + -1q = 0

Solving
-14 + -1q = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1q = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1q = 0 + 14
-1q = 0 + 14

Combine like terms: 0 + 14 = 14
-1q = 14

Divide each side by '-1'.
q = -14

Simplifying
q = -14
Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve:

Simplifying
1 + -2q = 0

Solving
1 + -2q = 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 + -2q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2q = 0 + -1
-2q = 0 + -1

Combine like terms: 0 + -1 = -1
-2q = -1

Divide each side by '-2'.
q = 0.5

Simplifying
q = 0.5
Solution
q = {-14, 0.5}