(3r+1)(2r-7)=

Solution for (3r+1)(2r-7)= equation:

Simplifying
(3r + 1)(2r + -7) = 0

Reorder the terms:
(1 + 3r)(2r + -7) = 0

Reorder the terms:
(1 + 3r)(-7 + 2r) = 0

Multiply (1 + 3r) * (-7 + 2r)
(1(-7 + 2r) + 3r * (-7 + 2r)) = 0
((-7 * 1 + 2r * 1) + 3r * (-7 + 2r)) = 0
((-7 + 2r) + 3r * (-7 + 2r)) = 0
(-7 + 2r + (-7 * 3r + 2r * 3r)) = 0
(-7 + 2r + (-21r + 6r2)) = 0

Combine like terms: 2r + -21r = -19r
(-7 + -19r + 6r2) = 0

Solving
-7 + -19r + 6r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-1 + -3r)(7 + -2r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -2r)' equal to zero and attempt to solve:

Simplifying
7 + -2r = 0

Solving
7 + -2r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2r = 0 + -7
-2r = 0 + -7

Combine like terms: 0 + -7 = -7
-2r = -7

Divide each side by '-2'.
r = 3.5

Simplifying
r = 3.5
Solution
r = {-0.3333333333, 3.5}