(5r-1)(2r+4)=

Solution for (5r-1)(2r+4)= equation:

Simplifying
(5r + -1)(2r + 4) = 0

Reorder the terms:
(-1 + 5r)(2r + 4) = 0

Reorder the terms:
(-1 + 5r)(4 + 2r) = 0

Multiply (-1 + 5r) * (4 + 2r)
(-1(4 + 2r) + 5r * (4 + 2r)) = 0
((4 * -1 + 2r * -1) + 5r * (4 + 2r)) = 0
((-4 + -2r) + 5r * (4 + 2r)) = 0
(-4 + -2r + (4 * 5r + 2r * 5r)) = 0
(-4 + -2r + (20r + 10r2)) = 0

Combine like terms: -2r + 20r = 18r
(-4 + 18r + 10r2) = 0

Solving
-4 + 18r + 10r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 9r + 5r2) = 0

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

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

Simplifying
-2 + -1r = 0

Solving
-2 + -1r = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1r = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1r = 0 + 2
-1r = 0 + 2

Combine like terms: 0 + 2 = 2
-1r = 2

Divide each side by '-1'.
r = -2

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

Simplifying
1 + -5r = 0

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

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

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

Divide each side by '-5'.
r = 0.2

Simplifying
r = 0.2
Solution
r = {-2, 0.2}