3r^2+4r=32

Solution for 3r^2+4r=32 equation:

Simplifying
3r2 + 4r = 32

Reorder the terms:
4r + 3r2 = 32

Solving
4r + 3r2 = 32

Solving for variable 'r'.

Reorder the terms:
-32 + 4r + 3r2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 4r + 3r2 = 0

Factor a trinomial.
(-4 + -1r)(8 + -3r) = 0

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

Simplifying
-4 + -1r = 0

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

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

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

Divide each side by '-1'.
r = -4

Simplifying
r = -4
Subproblem 2
Set the factor '(8 + -3r)' equal to zero and attempt to solve:

Simplifying
8 + -3r = 0

Solving
8 + -3r = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3r = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3r = 0 + -8
-3r = 0 + -8

Combine like terms: 0 + -8 = -8
-3r = -8

Divide each side by '-3'.
r = 2.666666667

Simplifying
r = 2.666666667
Solution
r = {-4, 2.666666667}