11r^2+6=-5r^2+50r

Solution for 11r^2+6=-5r^2+50r equation:

Simplifying
11r2 + 6 = -5r2 + 50r

Reorder the terms:
6 + 11r2 = -5r2 + 50r

Reorder the terms:
6 + 11r2 = 50r + -5r2

Solving
6 + 11r2 = 50r + -5r2

Solving for variable 'r'.

Reorder the terms:
6 + -50r + 11r2 + 5r2 = 50r + -5r2 + -50r + 5r2

Combine like terms: 11r2 + 5r2 = 16r2
6 + -50r + 16r2 = 50r + -5r2 + -50r + 5r2

Reorder the terms:
6 + -50r + 16r2 = 50r + -50r + -5r2 + 5r2

Combine like terms: 50r + -50r = 0
6 + -50r + 16r2 = 0 + -5r2 + 5r2
6 + -50r + 16r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
6 + -50r + 16r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -25r + 8r2) = 0

Factor a trinomial.
2((1 + -8r)(3 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -8r)' equal to zero and attempt to solve:

Simplifying
1 + -8r = 0

Solving
1 + -8r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -8r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8r = 0 + -1
-8r = 0 + -1

Combine like terms: 0 + -1 = -1
-8r = -1

Divide each side by '-8'.
r = 0.125

Simplifying
r = 0.125
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0.125, 3}