3q^2-7q+4=0

Solution for 3q^2-7q+4=0 equation:

Simplifying
3q2 + -7q + 4 = 0

Reorder the terms:
4 + -7q + 3q2 = 0

Solving
4 + -7q + 3q2 = 0

Solving for variable 'q'.

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

Subproblem 1
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
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 = {1, 1.333333333}