(3r-4)(r+1)=0

Solution for (3r-4)(r+1)=0 equation:

Simplifying
(3r + -4)(r + 1) = 0

Reorder the terms:
(-4 + 3r)(r + 1) = 0

Reorder the terms:
(-4 + 3r)(1 + r) = 0

Multiply (-4 + 3r) * (1 + r)
(-4(1 + r) + 3r * (1 + r)) = 0
((1 * -4 + r * -4) + 3r * (1 + r)) = 0
((-4 + -4r) + 3r * (1 + r)) = 0
(-4 + -4r + (1 * 3r + r * 3r)) = 0
(-4 + -4r + (3r + 3r2)) = 0

Combine like terms: -4r + 3r = -1r
(-4 + -1r + 3r2) = 0

Solving
-4 + -1r + 3r2 = 0

Solving for variable 'r'.

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

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 '(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
Solution
r = {-1, 1.333333333}