r^2+5r-1=-5r^2

Solution for r^2+5r-1=-5r^2 equation:

Simplifying
r2 + 5r + -1 = -5r2

Reorder the terms:
-1 + 5r + r2 = -5r2

Solving
-1 + 5r + r2 = -5r2

Solving for variable 'r'.

Combine like terms: r2 + 5r2 = 6r2
-1 + 5r + 6r2 = -5r2 + 5r2

Combine like terms: -5r2 + 5r2 = 0
-1 + 5r + 6r2 = 0

Factor a trinomial.
(-1 + -1r)(1 + -6r) = 0

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

Simplifying
-1 + -1r = 0

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

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

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

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

Simplifying
r = -1
Subproblem 2
Set the factor '(1 + -6r)' equal to zero and attempt to solve:

Simplifying
1 + -6r = 0

Solving
1 + -6r = 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 + -6r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6r = 0 + -1
-6r = 0 + -1

Combine like terms: 0 + -1 = -1
-6r = -1

Divide each side by '-6'.
r = 0.1666666667

Simplifying
r = 0.1666666667
Solution
r = {-1, 0.1666666667}