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

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

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

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

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

Multiply (4 + 3r) * (-5 + r)
(4(-5 + r) + 3r * (-5 + r)) = 0
((-5 * 4 + r * 4) + 3r * (-5 + r)) = 0
((-20 + 4r) + 3r * (-5 + r)) = 0
(-20 + 4r + (-5 * 3r + r * 3r)) = 0
(-20 + 4r + (-15r + 3r2)) = 0

Combine like terms: 4r + -15r = -11r
(-20 + -11r + 3r2) = 0

Solving
-20 + -11r + 3r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-4 + -3r = 0

Solving
-4 + -3r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3r = 0 + 4
-3r = 0 + 4

Combine like terms: 0 + 4 = 4
-3r = 4

Divide each side by '-3'.
r = -1.333333333

Simplifying
r = -1.333333333
Subproblem 2
Set the factor '(5 + -1r)' equal to zero and attempt to solve:

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {-1.333333333, 5}