10=r^2+3r

Solution for 10=r^2+3r equation:

Simplifying
10 = r2 + 3r

Reorder the terms:
10 = 3r + r2

Solving
10 = 3r + r2

Solving for variable 'r'.

Reorder the terms:
10 + -3r + -1r2 = 3r + -3r + r2 + -1r2

Combine like terms: 3r + -3r = 0
10 + -3r + -1r2 = 0 + r2 + -1r2
10 + -3r + -1r2 = r2 + -1r2

Combine like terms: r2 + -1r2 = 0
10 + -3r + -1r2 = 0

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

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

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

Simplifying
5 + r = 0

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

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

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

Simplifying
r = -5
Solution
r = {2, -5}