7q^2+51q+14=

Solution for 7q^2+51q+14= equation:

Simplifying
7q2 + 51q + 14 = 0

Reorder the terms:
14 + 51q + 7q2 = 0

Solving
14 + 51q + 7q2 = 0

Solving for variable 'q'.

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

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

Simplifying
7 + q = 0

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

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

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

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

Simplifying
2 + 7q = 0

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

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

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

Divide each side by '7'.
q = -0.2857142857

Simplifying
q = -0.2857142857
Solution
q = {-7, -0.2857142857}