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

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

Solving for variable 'r'.

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

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + r + 30r2)' equal to zero and attempt to solve:

Simplifying
1 + r + 30r2 = 0

Solving
1 + r + 30r2 = 0

Begin completing the square.  Divide all terms by
30 the coefficient of the squared term: 

Divide each side by '30'.
0.03333333333 + 0.03333333333r + r2 = 0.0

Move the constant term to the right:

Add '-0.03333333333' to each side of the equation.
0.03333333333 + 0.03333333333r + -0.03333333333 + r2 = 0.0 + -0.03333333333

Reorder the terms:
0.03333333333 + -0.03333333333 + 0.03333333333r + r2 = 0.0 + -0.03333333333

Combine like terms: 0.03333333333 + -0.03333333333 = 0.00000000000
0.00000000000 + 0.03333333333r + r2 = 0.0 + -0.03333333333
0.03333333333r + r2 = 0.0 + -0.03333333333

Combine like terms: 0.0 + -0.03333333333 = -0.03333333333
0.03333333333r + r2 = -0.03333333333

The r term is r.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.03333333333r + 0.25 + r2 = -0.03333333333 + 0.25

Reorder the terms:
0.25 + 0.03333333333r + r2 = -0.03333333333 + 0.25

Combine like terms: -0.03333333333 + 0.25 = 0.21666666667
0.25 + 0.03333333333r + r2 = 0.21666666667

Factor a perfect square on the left side:
(r + 0.5)(r + 0.5) = 0.21666666667

Calculate the square root of the right side: 0.465474668

Break this problem into two subproblems by setting 
(r + 0.5) equal to 0.465474668 and -0.465474668.

Subproblem 1
r + 0.5 = 0.465474668

Simplifying
r + 0.5 = 0.465474668

Reorder the terms:
0.5 + r = 0.465474668

Solving
0.5 + r = 0.465474668

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = 0.465474668 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = 0.465474668 + -0.5
r = 0.465474668 + -0.5

Combine like terms: 0.465474668 + -0.5 = -0.034525332
r = -0.034525332

Simplifying
r = -0.034525332

Subproblem 2
r + 0.5 = -0.465474668

Simplifying
r + 0.5 = -0.465474668

Reorder the terms:
0.5 + r = -0.465474668

Solving
0.5 + r = -0.465474668

Solving for variable 'r'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + r = -0.465474668 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + r = -0.465474668 + -0.5
r = -0.465474668 + -0.5

Combine like terms: -0.465474668 + -0.5 = -0.965474668
r = -0.965474668

Simplifying
r = -0.965474668

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {-0.034525332, -0.965474668}
Solution
r = {-0.034525332, -0.965474668}