-6r(1+5r)-(1+5r)=

Solution for -6r(1+5r)-(1+5r)= equation:

Simplifying
-6r(1 + 5r) + -1(1 + 5r) = 0
(1 * -6r + 5r * -6r) + -1(1 + 5r) = 0
(-6r + -30r2) + -1(1 + 5r) = 0
-6r + -30r2 + (1 * -1 + 5r * -1) = 0
-6r + -30r2 + (-1 + -5r) = 0

Reorder the terms:
-1 + -6r + -5r + -30r2 = 0

Combine like terms: -6r + -5r = -11r
-1 + -11r + -30r2 = 0

Solving
-1 + -11r + -30r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 11r + 30r2) = 0

Factor a trinomial.
-1((1 + 5r)(1 + 6r)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 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 + 5r = 0 + -1

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

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

Divide each side by '5'.
r = -0.2

Simplifying
r = -0.2
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 = {-0.2, -0.1666666667}