5r^2=r+4

Solution for 5r^2=r+4 equation:

Simplifying
5r2 = r + 4

Reorder the terms:
5r2 = 4 + r

Solving
5r2 = 4 + r

Solving for variable 'r'.

Reorder the terms:
-4 + -1r + 5r2 = 4 + r + -4 + -1r

Reorder the terms:
-4 + -1r + 5r2 = 4 + -4 + r + -1r

Combine like terms: 4 + -4 = 0
-4 + -1r + 5r2 = 0 + r + -1r
-4 + -1r + 5r2 = r + -1r

Combine like terms: r + -1r = 0
-4 + -1r + 5r2 = 0

Factor a trinomial.
(-4 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(-4 + -5r)' equal to zero and attempt to solve:

Simplifying
-4 + -5r = 0

Solving
-4 + -5r = 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 + -5r = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5r = 0 + 4
-5r = 0 + 4

Combine like terms: 0 + 4 = 4
-5r = 4

Divide each side by '-5'.
r = -0.8

Simplifying
r = -0.8
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 = {-0.8, 1}