14r^2+26r+6=3r-7r^2

Solution for 14r^2+26r+6=3r-7r^2 equation:

Simplifying
14r2 + 26r + 6 = 3r + -7r2

Reorder the terms:
6 + 26r + 14r2 = 3r + -7r2

Solving
6 + 26r + 14r2 = 3r + -7r2

Solving for variable 'r'.

Reorder the terms:
6 + 26r + -3r + 14r2 + 7r2 = 3r + -7r2 + -3r + 7r2

Combine like terms: 26r + -3r = 23r
6 + 23r + 14r2 + 7r2 = 3r + -7r2 + -3r + 7r2

Combine like terms: 14r2 + 7r2 = 21r2
6 + 23r + 21r2 = 3r + -7r2 + -3r + 7r2

Reorder the terms:
6 + 23r + 21r2 = 3r + -3r + -7r2 + 7r2

Combine like terms: 3r + -3r = 0
6 + 23r + 21r2 = 0 + -7r2 + 7r2
6 + 23r + 21r2 = -7r2 + 7r2

Combine like terms: -7r2 + 7r2 = 0
6 + 23r + 21r2 = 0

Factor a trinomial.
(2 + 3r)(3 + 7r) = 0

Subproblem 1
Set the factor '(2 + 3r)' equal to zero and attempt to solve:

Simplifying
2 + 3r = 0

Solving
2 + 3r = 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 + 3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3r = 0 + -2
3r = 0 + -2

Combine like terms: 0 + -2 = -2
3r = -2

Divide each side by '3'.
r = -0.6666666667

Simplifying
r = -0.6666666667
Subproblem 2
Set the factor '(3 + 7r)' equal to zero and attempt to solve:

Simplifying
3 + 7r = 0

Solving
3 + 7r = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7r = 0 + -3

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

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

Divide each side by '7'.
r = -0.4285714286

Simplifying
r = -0.4285714286
Solution
r = {-0.6666666667, -0.4285714286}