3q^2+q=14

Solution for 3q^2+q=14 equation:

Simplifying
3q2 + q = 14

Reorder the terms:
q + 3q2 = 14

Solving
q + 3q2 = 14

Solving for variable 'q'.

Reorder the terms:
-14 + q + 3q2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + q + 3q2 = 0

Factor a trinomial.
(-7 + -3q)(2 + -1q) = 0

Subproblem 1
Set the factor '(-7 + -3q)' equal to zero and attempt to solve:

Simplifying
-7 + -3q = 0

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

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

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

Divide each side by '-3'.
q = -2.333333333

Simplifying
q = -2.333333333
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 = {-2.333333333, 2}