r^2-24r-6=-5r-6r^2

Solution for r^2-24r-6=-5r-6r^2 equation:

Simplifying
r2 + -24r + -6 = -5r + -6r2

Reorder the terms:
-6 + -24r + r2 = -5r + -6r2

Solving
-6 + -24r + r2 = -5r + -6r2

Solving for variable 'r'.

Reorder the terms:
-6 + -24r + 5r + r2 + 6r2 = -5r + -6r2 + 5r + 6r2

Combine like terms: -24r + 5r = -19r
-6 + -19r + r2 + 6r2 = -5r + -6r2 + 5r + 6r2

Combine like terms: r2 + 6r2 = 7r2
-6 + -19r + 7r2 = -5r + -6r2 + 5r + 6r2

Reorder the terms:
-6 + -19r + 7r2 = -5r + 5r + -6r2 + 6r2

Combine like terms: -5r + 5r = 0
-6 + -19r + 7r2 = 0 + -6r2 + 6r2
-6 + -19r + 7r2 = -6r2 + 6r2

Combine like terms: -6r2 + 6r2 = 0
-6 + -19r + 7r2 = 0

Factor a trinomial.
(-2 + -7r)(3 + -1r) = 0

Subproblem 1
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
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 = {-0.2857142857, 3}