12r^2+13r=4

Solution for 12r^2+13r=4 equation:

Simplifying
12r2 + 13r = 4

Reorder the terms:
13r + 12r2 = 4

Solving
13r + 12r2 = 4

Solving for variable 'r'.

Reorder the terms:
-4 + 13r + 12r2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 13r + 12r2 = 0

Factor a trinomial.
(-4 + -3r)(1 + -4r) = 0

Subproblem 1
Set the factor '(-4 + -3r)' equal to zero and attempt to solve:

Simplifying
-4 + -3r = 0

Solving
-4 + -3r = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3r = 0 + 4
-3r = 0 + 4

Combine like terms: 0 + 4 = 4
-3r = 4

Divide each side by '-3'.
r = -1.333333333

Simplifying
r = -1.333333333
Subproblem 2
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 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 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Solution
r = {-1.333333333, 0.25}