(4r-4)(5r-6)=0

Solution for (4r-4)(5r-6)=0 equation:

Simplifying
(4r + -4)(5r + -6) = 0

Reorder the terms:
(-4 + 4r)(5r + -6) = 0

Reorder the terms:
(-4 + 4r)(-6 + 5r) = 0

Multiply (-4 + 4r) * (-6 + 5r)
(-4(-6 + 5r) + 4r * (-6 + 5r)) = 0
((-6 * -4 + 5r * -4) + 4r * (-6 + 5r)) = 0
((24 + -20r) + 4r * (-6 + 5r)) = 0
(24 + -20r + (-6 * 4r + 5r * 4r)) = 0
(24 + -20r + (-24r + 20r2)) = 0

Combine like terms: -20r + -24r = -44r
(24 + -44r + 20r2) = 0

Solving
24 + -44r + 20r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -11r + 5r2) = 0

Factor a trinomial.
4((1 + -1r)(6 + -5r)) = 0

Ignore the factor 4.
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 '(6 + -5r)' equal to zero and attempt to solve:

Simplifying
6 + -5r = 0

Solving
6 + -5r = 0

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

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

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

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

Divide each side by '-5'.
r = 1.2

Simplifying
r = 1.2
Solution
r = {1, 1.2}