7r^2+51r+14=

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

Simplifying
7r2 + 51r + 14 = 0

Reorder the terms:
14 + 51r + 7r2 = 0

Solving
14 + 51r + 7r2 = 0

Solving for variable 'r'.

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

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

Simplifying
7 + r = 0

Solving
7 + r = 0

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

Add '-7' to each side of the equation.
7 + -7 + r = 0 + -7

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

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

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

Simplifying
2 + 7r = 0

Solving
2 + 7r = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7r = 0 + -2

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

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

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

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