4r^2-3=11r

Solution for 4r^2-3=11r equation:

Simplifying
4r2 + -3 = 11r

Reorder the terms:
-3 + 4r2 = 11r

Solving
-3 + 4r2 = 11r

Solving for variable 'r'.

Reorder the terms:
-3 + -11r + 4r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
-3 + -11r + 4r2 = 0

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-0.25, 3}