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

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

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

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

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

Multiply (-2 + 4r) * (2 + 5r)
(-2(2 + 5r) + 4r * (2 + 5r)) = 0
((2 * -2 + 5r * -2) + 4r * (2 + 5r)) = 0
((-4 + -10r) + 4r * (2 + 5r)) = 0
(-4 + -10r + (2 * 4r + 5r * 4r)) = 0
(-4 + -10r + (8r + 20r2)) = 0

Combine like terms: -10r + 8r = -2r
(-4 + -2r + 20r2) = 0

Solving
-4 + -2r + 20r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -1r + 10r2) = 0

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

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

Simplifying
-2 + -5r = 0

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

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

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

Divide each side by '-5'.
r = -0.4

Simplifying
r = -0.4
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 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 + -2r = 0 + -1

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {-0.4, 0.5}