6q^2-11q+4=0

Solution for 6q^2-11q+4=0 equation:

Simplifying
6q2 + -11q + 4 = 0

Reorder the terms:
4 + -11q + 6q2 = 0

Solving
4 + -11q + 6q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(1 + -2q)(4 + -3q) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -3q)' equal to zero and attempt to solve:

Simplifying
4 + -3q = 0

Solving
4 + -3q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3q = 0 + -4
-3q = 0 + -4

Combine like terms: 0 + -4 = -4
-3q = -4

Divide each side by '-3'.
q = 1.333333333

Simplifying
q = 1.333333333
Solution
q = {0.5, 1.333333333}