(2r-6)(3r+4)=-20

Solution for (2r-6)(3r+4)=-20 equation:

Simplifying
(2r + -6)(3r + 4) = -20

Reorder the terms:
(-6 + 2r)(3r + 4) = -20

Reorder the terms:
(-6 + 2r)(4 + 3r) = -20

Multiply (-6 + 2r) * (4 + 3r)
(-6(4 + 3r) + 2r * (4 + 3r)) = -20
((4 * -6 + 3r * -6) + 2r * (4 + 3r)) = -20
((-24 + -18r) + 2r * (4 + 3r)) = -20
(-24 + -18r + (4 * 2r + 3r * 2r)) = -20
(-24 + -18r + (8r + 6r2)) = -20

Combine like terms: -18r + 8r = -10r
(-24 + -10r + 6r2) = -20

Solving
-24 + -10r + 6r2 = -20

Solving for variable 'r'.

Reorder the terms:
-24 + 20 + -10r + 6r2 = -20 + 20

Combine like terms: -24 + 20 = -4
-4 + -10r + 6r2 = -20 + 20

Combine like terms: -20 + 20 = 0
-4 + -10r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5r + 3r2) = 0

Factor a trinomial.
2((-1 + -3r)(2 + -1r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3r)' equal to zero and attempt to solve:

Simplifying
-1 + -3r = 0

Solving
-1 + -3r = 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 + -3r = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3r = 0 + 1
-3r = 0 + 1

Combine like terms: 0 + 1 = 1
-3r = 1

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-0.3333333333, 2}