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

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

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

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

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

Multiply (-2 + 3r) * (2 + 7r)
(-2(2 + 7r) + 3r * (2 + 7r)) = 0
((2 * -2 + 7r * -2) + 3r * (2 + 7r)) = 0
((-4 + -14r) + 3r * (2 + 7r)) = 0
(-4 + -14r + (2 * 3r + 7r * 3r)) = 0
(-4 + -14r + (6r + 21r2)) = 0

Combine like terms: -14r + 6r = -8r
(-4 + -8r + 21r2) = 0

Solving
-4 + -8r + 21r2 = 0

Solving for variable 'r'.

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

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

Simplifying
-2 + -7r = 0

Solving
-2 + -7r = 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 + -7r = 0 + 2

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

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

Divide each side by '-7'.
r = -0.2857142857

Simplifying
r = -0.2857142857
Subproblem 2
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 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 + -3r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3r = 0 + -2
-3r = 0 + -2

Combine like terms: 0 + -2 = -2
-3r = -2

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {-0.2857142857, 0.6666666667}