(12r+7)(5r-6)=0

Solution for (12r+7)(5r-6)=0 equation:

Simplifying
(12r + 7)(5r + -6) = 0

Reorder the terms:
(7 + 12r)(5r + -6) = 0

Reorder the terms:
(7 + 12r)(-6 + 5r) = 0

Multiply (7 + 12r) * (-6 + 5r)
(7(-6 + 5r) + 12r * (-6 + 5r)) = 0
((-6 * 7 + 5r * 7) + 12r * (-6 + 5r)) = 0
((-42 + 35r) + 12r * (-6 + 5r)) = 0
(-42 + 35r + (-6 * 12r + 5r * 12r)) = 0
(-42 + 35r + (-72r + 60r2)) = 0

Combine like terms: 35r + -72r = -37r
(-42 + -37r + 60r2) = 0

Solving
-42 + -37r + 60r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -12r)(6 + -5r) = 0

Subproblem 1
Set the factor '(-7 + -12r)' equal to zero and attempt to solve:

Simplifying
-7 + -12r = 0

Solving
-7 + -12r = 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 + -12r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12r = 0 + 7
-12r = 0 + 7

Combine like terms: 0 + 7 = 7
-12r = 7

Divide each side by '-12'.
r = -0.5833333333

Simplifying
r = -0.5833333333
Subproblem 2
Set the factor '(6 + -5r)' equal to zero and attempt to solve:

Simplifying
6 + -5r = 0

Solving
6 + -5r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5r = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5r = 0 + -6
-5r = 0 + -6

Combine like terms: 0 + -6 = -6
-5r = -6

Divide each side by '-5'.
r = 1.2

Simplifying
r = 1.2
Solution
r = {-0.5833333333, 1.2}