2q^2-11q+14=0

Solution for 2q^2-11q+14=0 equation:

Simplifying
2q2 + -11q + 14 = 0

Reorder the terms:
14 + -11q + 2q2 = 0

Solving
14 + -11q + 2q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + -1q)(7 + -2q) = 0

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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

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

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

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Subproblem 2
Set the factor '(7 + -2q)' equal to zero and attempt to solve:

Simplifying
7 + -2q = 0

Solving
7 + -2q = 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 + -2q = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2q = 0 + -7
-2q = 0 + -7

Combine like terms: 0 + -7 = -7
-2q = -7

Divide each side by '-2'.
q = 3.5

Simplifying
q = 3.5
Solution
q = {2, 3.5}