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

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

Simplifying
2(r + 3) + 5(r + -2) = 10

Reorder the terms:
2(3 + r) + 5(r + -2) = 10
(3 * 2 + r * 2) + 5(r + -2) = 10
(6 + 2r) + 5(r + -2) = 10

Reorder the terms:
6 + 2r + 5(-2 + r) = 10
6 + 2r + (-2 * 5 + r * 5) = 10
6 + 2r + (-10 + 5r) = 10

Reorder the terms:
6 + -10 + 2r + 5r = 10

Combine like terms: 6 + -10 = -4
-4 + 2r + 5r = 10

Combine like terms: 2r + 5r = 7r
-4 + 7r = 10

Solving
-4 + 7r = 10

Solving for variable 'r'.

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

Add '4' to each side of the equation.
-4 + 4 + 7r = 10 + 4

Combine like terms: -4 + 4 = 0
0 + 7r = 10 + 4
7r = 10 + 4

Combine like terms: 10 + 4 = 14
7r = 14

Divide each side by '7'.
r = 2

Simplifying
r = 2