=3r^2+5r-12

Solution for =3r^2+5r-12 equation:

Simplifying
0 = 3r2 + 5r + -12

Reorder the terms:
0 = -12 + 5r + 3r2

Solving
0 = -12 + 5r + 3r2

Solving for variable 'r'.

Combine like terms: 0 + 12 = 12
12 + -5r + -3r2 = -12 + 5r + 3r2 + 12 + -5r + -3r2

Reorder the terms:
12 + -5r + -3r2 = -12 + 12 + 5r + -5r + 3r2 + -3r2

Combine like terms: -12 + 12 = 0
12 + -5r + -3r2 = 0 + 5r + -5r + 3r2 + -3r2
12 + -5r + -3r2 = 5r + -5r + 3r2 + -3r2

Combine like terms: 5r + -5r = 0
12 + -5r + -3r2 = 0 + 3r2 + -3r2
12 + -5r + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
12 + -5r + -3r2 = 0

Factor a trinomial.
(4 + -3r)(3 + r) = 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 '(3 + r)' equal to zero and attempt to solve:

Simplifying
3 + r = 0

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

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

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

Simplifying
r = -3
Solution
r = {1.333333333, -3}