4r^2=r+3

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

Simplifying
4r2 = r + 3

Reorder the terms:
4r2 = 3 + r

Solving
4r2 = 3 + r

Solving for variable 'r'.

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

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

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

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

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

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

Simplifying
-3 + -4r = 0

Solving
-3 + -4r = 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 + -4r = 0 + 3

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

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

Divide each side by '-4'.
r = -0.75

Simplifying
r = -0.75
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 = {-0.75, 1}