-6r(r+4)=-30

Solution for -6r(r+4)=-30 equation:

Simplifying
-6r(r + 4) = -30

Reorder the terms:
-6r(4 + r) = -30
(4 * -6r + r * -6r) = -30
(-24r + -6r2) = -30

Solving
-24r + -6r2 = -30

Solving for variable 'r'.

Reorder the terms:
30 + -24r + -6r2 = -30 + 30

Combine like terms: -30 + 30 = 0
30 + -24r + -6r2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -4r + -1r2) = 0

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

Ignore the factor 6.
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 '(5 + r)' equal to zero and attempt to solve:

Simplifying
5 + r = 0

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

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

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

Simplifying
r = -5
Solution
r = {1, -5}