5(r-3)=10(r^2-3)

Solution for 5(r-3)=10(r^2-3) equation:

Simplifying
5(r + -3) = 10(r2 + -3)

Reorder the terms:
5(-3 + r) = 10(r2 + -3)
(-3 * 5 + r * 5) = 10(r2 + -3)
(-15 + 5r) = 10(r2 + -3)

Reorder the terms:
-15 + 5r = 10(-3 + r2)
-15 + 5r = (-3 * 10 + r2 * 10)
-15 + 5r = (-30 + 10r2)

Solving
-15 + 5r = -30 + 10r2

Solving for variable 'r'.

Reorder the terms:
-15 + 30 + 5r + -10r2 = -30 + 10r2 + 30 + -10r2

Combine like terms: -15 + 30 = 15
15 + 5r + -10r2 = -30 + 10r2 + 30 + -10r2

Reorder the terms:
15 + 5r + -10r2 = -30 + 30 + 10r2 + -10r2

Combine like terms: -30 + 30 = 0
15 + 5r + -10r2 = 0 + 10r2 + -10r2
15 + 5r + -10r2 = 10r2 + -10r2

Combine like terms: 10r2 + -10r2 = 0
15 + 5r + -10r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + r + -2r2) = 0

Factor a trinomial.
5((3 + -2r)(1 + r)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Subproblem 2
Set the factor '(1 + r)' equal to zero and attempt to solve:

Simplifying
1 + r = 0

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

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

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

Simplifying
r = -1
Solution
r = {1.5, -1}