0=-3q^2+7q-2

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

Simplifying
0 = -3q2 + 7q + -2

Reorder the terms:
0 = -2 + 7q + -3q2

Solving
0 = -2 + 7q + -3q2

Solving for variable 'q'.

Combine like terms: 0 + 2 = 2
2 + -7q + 3q2 = -2 + 7q + -3q2 + 2 + -7q + 3q2

Reorder the terms:
2 + -7q + 3q2 = -2 + 2 + 7q + -7q + -3q2 + 3q2

Combine like terms: -2 + 2 = 0
2 + -7q + 3q2 = 0 + 7q + -7q + -3q2 + 3q2
2 + -7q + 3q2 = 7q + -7q + -3q2 + 3q2

Combine like terms: 7q + -7q = 0
2 + -7q + 3q2 = 0 + -3q2 + 3q2
2 + -7q + 3q2 = -3q2 + 3q2

Combine like terms: -3q2 + 3q2 = 0
2 + -7q + 3q2 = 0

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

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

Simplifying
1 + -3q = 0

Solving
1 + -3q = 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 + -3q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3q = 0 + -1
-3q = 0 + -1

Combine like terms: 0 + -1 = -1
-3q = -1

Divide each side by '-3'.
q = 0.3333333333

Simplifying
q = 0.3333333333
Subproblem 2
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
Solution
q = {0.3333333333, 2}