r(12r+5)=7

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

Simplifying
r(12r + 5) = 7

Reorder the terms:
r(5 + 12r) = 7
(5 * r + 12r * r) = 7
(5r + 12r2) = 7

Solving
5r + 12r2 = 7

Solving for variable 'r'.

Reorder the terms:
-7 + 5r + 12r2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 5r + 12r2 = 0

Factor a trinomial.
(-1 + -1r)(7 + -12r) = 0

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

Simplifying
-1 + -1r = 0

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

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

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

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

Simplifying
r = -1
Subproblem 2
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
Solution
r = {-1, 0.5833333333}