(13r+7)(6r-18)=0

Solution for (13r+7)(6r-18)=0 equation:

Simplifying
(13r + 7)(6r + -18) = 0

Reorder the terms:
(7 + 13r)(6r + -18) = 0

Reorder the terms:
(7 + 13r)(-18 + 6r) = 0

Multiply (7 + 13r) * (-18 + 6r)
(7(-18 + 6r) + 13r * (-18 + 6r)) = 0
((-18 * 7 + 6r * 7) + 13r * (-18 + 6r)) = 0
((-126 + 42r) + 13r * (-18 + 6r)) = 0
(-126 + 42r + (-18 * 13r + 6r * 13r)) = 0
(-126 + 42r + (-234r + 78r2)) = 0

Combine like terms: 42r + -234r = -192r
(-126 + -192r + 78r2) = 0

Solving
-126 + -192r + 78r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + -32r + 13r2) = 0

Factor a trinomial.
6((-7 + -13r)(3 + -1r)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -13r)' equal to zero and attempt to solve:

Simplifying
-7 + -13r = 0

Solving
-7 + -13r = 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 + -13r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13r = 0 + 7
-13r = 0 + 7

Combine like terms: 0 + 7 = 7
-13r = 7

Divide each side by '-13'.
r = -0.5384615385

Simplifying
r = -0.5384615385
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r = 0 + -3

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.5384615385, 3}