(4r-3)(3r+2r+5)=

Solution for (4r-3)(3r+2r+5)= equation:

Simplifying
(4r + -3)(3r + 2r + 5) = 0

Reorder the terms:
(-3 + 4r)(3r + 2r + 5) = 0

Reorder the terms:
(-3 + 4r)(5 + 3r + 2r) = 0

Combine like terms: 3r + 2r = 5r
(-3 + 4r)(5 + 5r) = 0

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

Combine like terms: -15r + 20r = 5r
(-15 + 5r + 20r2) = 0

Solving
-15 + 5r + 20r2 = 0

Solving for variable 'r'.

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

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

Ignore the factor 5.
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 '(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 = {-1, 0.75}