(3r-3)(4r+5)=0

Solution for (3r-3)(4r+5)=0 equation:

Simplifying
(3r + -3)(4r + 5) = 0

Reorder the terms:
(-3 + 3r)(4r + 5) = 0

Reorder the terms:
(-3 + 3r)(5 + 4r) = 0

Multiply (-3 + 3r) * (5 + 4r)
(-3(5 + 4r) + 3r * (5 + 4r)) = 0
((5 * -3 + 4r * -3) + 3r * (5 + 4r)) = 0
((-15 + -12r) + 3r * (5 + 4r)) = 0
(-15 + -12r + (5 * 3r + 4r * 3r)) = 0
(-15 + -12r + (15r + 12r2)) = 0

Combine like terms: -12r + 15r = 3r
(-15 + 3r + 12r2) = 0

Solving
-15 + 3r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + r + 4r2) = 0

Factor a trinomial.
3((-5 + -4r)(1 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -4r)' equal to zero and attempt to solve:

Simplifying
-5 + -4r = 0

Solving
-5 + -4r = 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 + -4r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4r = 0 + 5
-4r = 0 + 5

Combine like terms: 0 + 5 = 5
-4r = 5

Divide each side by '-4'.
r = -1.25

Simplifying
r = -1.25
Subproblem 2
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
Solution
r = {-1.25, 1}