24r=5(r^2-1)

Solution for 24r=5(r^2-1) equation:

Simplifying
24r = 5(r2 + -1)

Reorder the terms:
24r = 5(-1 + r2)
24r = (-1 * 5 + r2 * 5)
24r = (-5 + 5r2)

Solving
24r = -5 + 5r2

Solving for variable 'r'.

Reorder the terms:
5 + 24r + -5r2 = -5 + 5r2 + 5 + -5r2

Reorder the terms:
5 + 24r + -5r2 = -5 + 5 + 5r2 + -5r2

Combine like terms: -5 + 5 = 0
5 + 24r + -5r2 = 0 + 5r2 + -5r2
5 + 24r + -5r2 = 5r2 + -5r2

Combine like terms: 5r2 + -5r2 = 0
5 + 24r + -5r2 = 0

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

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

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Subproblem 2
Set the factor '(1 + 5r)' equal to zero and attempt to solve:

Simplifying
1 + 5r = 0

Solving
1 + 5r = 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 + 5r = 0 + -1

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

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

Divide each side by '5'.
r = -0.2

Simplifying
r = -0.2
Solution
r = {5, -0.2}