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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
r = {-0.2, 2}