3r^2=4r-1

Solution for 3r^2=4r-1 equation:

Simplifying
3r2 = 4r + -1

Reorder the terms:
3r2 = -1 + 4r

Solving
3r2 = -1 + 4r

Solving for variable 'r'.

Reorder the terms:
1 + -4r + 3r2 = -1 + 4r + 1 + -4r

Reorder the terms:
1 + -4r + 3r2 = -1 + 1 + 4r + -4r

Combine like terms: -1 + 1 = 0
1 + -4r + 3r2 = 0 + 4r + -4r
1 + -4r + 3r2 = 4r + -4r

Combine like terms: 4r + -4r = 0
1 + -4r + 3r2 = 0

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

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

Simplifying
1 + -3r = 0

Solving
1 + -3r = 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 + -3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3r = 0 + -1
-3r = 0 + -1

Combine like terms: 0 + -1 = -1
-3r = -1

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Subproblem 2
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
Solution
r = {0.3333333333, 1}