(1+3r)(2-r)=

Solution for (1+3r)(2-r)= equation:

Simplifying
(1 + 3r)(2 + -1r) = 0

Multiply (1 + 3r) * (2 + -1r)
(1(2 + -1r) + 3r * (2 + -1r)) = 0
((2 * 1 + -1r * 1) + 3r * (2 + -1r)) = 0
((2 + -1r) + 3r * (2 + -1r)) = 0
(2 + -1r + (2 * 3r + -1r * 3r)) = 0
(2 + -1r + (6r + -3r2)) = 0

Combine like terms: -1r + 6r = 5r
(2 + 5r + -3r2) = 0

Solving
2 + 5r + -3r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2 + -1r)(1 + 3r) = 0

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 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {2, -0.3333333333}