(r-4)*(2r+5)=0

Solution for (r-4)*(2r+5)=0 equation:

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

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

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

Multiply (-4 + r) * (5 + 2r)
(-4(5 + 2r) + r(5 + 2r)) = 0
((5 * -4 + 2r * -4) + r(5 + 2r)) = 0
((-20 + -8r) + r(5 + 2r)) = 0
(-20 + -8r + (5 * r + 2r * r)) = 0
(-20 + -8r + (5r + 2r2)) = 0

Combine like terms: -8r + 5r = -3r
(-20 + -3r + 2r2) = 0

Solving
-20 + -3r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-5 + -2r)(4 + -1r) = 0

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

Simplifying
-5 + -2r = 0

Solving
-5 + -2r = 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 + -2r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2r = 0 + 5
-2r = 0 + 5

Combine like terms: 0 + 5 = 5
-2r = 5

Divide each side by '-2'.
r = -2.5

Simplifying
r = -2.5
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

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

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {-2.5, 4}