5r(r+1)-r(3-2r)=

Solution for 5r(r+1)-r(3-2r)= equation:

Simplifying
5r(r + 1) + -1r(3 + -2r) = 0

Reorder the terms:
5r(1 + r) + -1r(3 + -2r) = 0
(1 * 5r + r * 5r) + -1r(3 + -2r) = 0
(5r + 5r2) + -1r(3 + -2r) = 0
5r + 5r2 + (3 * -1r + -2r * -1r) = 0
5r + 5r2 + (-3r + 2r2) = 0

Reorder the terms:
5r + -3r + 5r2 + 2r2 = 0

Combine like terms: 5r + -3r = 2r
2r + 5r2 + 2r2 = 0

Combine like terms: 5r2 + 2r2 = 7r2
2r + 7r2 = 0

Solving
2r + 7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(2 + 7r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(2 + 7r)' equal to zero and attempt to solve:

Simplifying
2 + 7r = 0

Solving
2 + 7r = 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 + 7r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7r = 0 + -2
7r = 0 + -2

Combine like terms: 0 + -2 = -2
7r = -2

Divide each side by '7'.
r = -0.2857142857

Simplifying
r = -0.2857142857
Solution
r = {0, -0.2857142857}