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

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

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

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

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

Multiply (4 + 5r) * (-3 + 4r)
(4(-3 + 4r) + 5r * (-3 + 4r)) = 0
((-3 * 4 + 4r * 4) + 5r * (-3 + 4r)) = 0
((-12 + 16r) + 5r * (-3 + 4r)) = 0
(-12 + 16r + (-3 * 5r + 4r * 5r)) = 0
(-12 + 16r + (-15r + 20r2)) = 0

Combine like terms: 16r + -15r = 1r
(-12 + 1r + 20r2) = 0

Solving
-12 + 1r + 20r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-4 + -5r = 0

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

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

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

Divide each side by '-5'.
r = -0.8

Simplifying
r = -0.8
Subproblem 2
Set the factor '(3 + -4r)' equal to zero and attempt to solve:

Simplifying
3 + -4r = 0

Solving
3 + -4r = 0

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

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

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

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

Divide each side by '-4'.
r = 0.75

Simplifying
r = 0.75
Solution
r = {-0.8, 0.75}