47r^2+315r+131=5-2r^2

Solution for 47r^2+315r+131=5-2r^2 equation:

Simplifying
47r2 + 315r + 131 = 5 + -2r2

Reorder the terms:
131 + 315r + 47r2 = 5 + -2r2

Solving
131 + 315r + 47r2 = 5 + -2r2

Solving for variable 'r'.

Reorder the terms:
131 + -5 + 315r + 47r2 + 2r2 = 5 + -2r2 + -5 + 2r2

Combine like terms: 131 + -5 = 126
126 + 315r + 47r2 + 2r2 = 5 + -2r2 + -5 + 2r2

Combine like terms: 47r2 + 2r2 = 49r2
126 + 315r + 49r2 = 5 + -2r2 + -5 + 2r2

Reorder the terms:
126 + 315r + 49r2 = 5 + -5 + -2r2 + 2r2

Combine like terms: 5 + -5 = 0
126 + 315r + 49r2 = 0 + -2r2 + 2r2
126 + 315r + 49r2 = -2r2 + 2r2

Combine like terms: -2r2 + 2r2 = 0
126 + 315r + 49r2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(18 + 45r + 7r2) = 0

Factor a trinomial.
7((6 + r)(3 + 7r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(6 + r)' equal to zero and attempt to solve:

Simplifying
6 + r = 0

Solving
6 + r = 0

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

Add '-6' to each side of the equation.
6 + -6 + r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + r = 0 + -6
r = 0 + -6

Combine like terms: 0 + -6 = -6
r = -6

Simplifying
r = -6
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 = {-6, -0.4285714286}