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

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

Simplifying
(6r + -5)(6r + 1) = 0

Reorder the terms:
(-5 + 6r)(6r + 1) = 0

Reorder the terms:
(-5 + 6r)(1 + 6r) = 0

Multiply (-5 + 6r) * (1 + 6r)
(-5(1 + 6r) + 6r * (1 + 6r)) = 0
((1 * -5 + 6r * -5) + 6r * (1 + 6r)) = 0
((-5 + -30r) + 6r * (1 + 6r)) = 0
(-5 + -30r + (1 * 6r + 6r * 6r)) = 0
(-5 + -30r + (6r + 36r2)) = 0

Combine like terms: -30r + 6r = -24r
(-5 + -24r + 36r2) = 0

Solving
-5 + -24r + 36r2 = 0

Solving for variable 'r'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -6r)' equal to zero and attempt to solve:

Simplifying
5 + -6r = 0

Solving
5 + -6r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6r = 0 + -5

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

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

Divide each side by '-6'.
r = 0.8333333333

Simplifying
r = 0.8333333333
Solution
r = {-0.1666666667, 0.8333333333}