(r-10)(6r+5)=0

Solution for (r-10)(6r+5)=0 equation:

Simplifying
(r + -10)(6r + 5) = 0

Reorder the terms:
(-10 + r)(6r + 5) = 0

Reorder the terms:
(-10 + r)(5 + 6r) = 0

Multiply (-10 + r) * (5 + 6r)
(-10(5 + 6r) + r(5 + 6r)) = 0
((5 * -10 + 6r * -10) + r(5 + 6r)) = 0
((-50 + -60r) + r(5 + 6r)) = 0
(-50 + -60r + (5 * r + 6r * r)) = 0
(-50 + -60r + (5r + 6r2)) = 0

Combine like terms: -60r + 5r = -55r
(-50 + -55r + 6r2) = 0

Solving
-50 + -55r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -6r)(10 + -1r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-0.8333333333, 10}