-10(r+1)-5r(1-5r)=

Solution for -10(r+1)-5r(1-5r)= equation:

Simplifying
-10(r + 1) + -5r(1 + -5r) = 0

Reorder the terms:
-10(1 + r) + -5r(1 + -5r) = 0
(1 * -10 + r * -10) + -5r(1 + -5r) = 0
(-10 + -10r) + -5r(1 + -5r) = 0
-10 + -10r + (1 * -5r + -5r * -5r) = 0
-10 + -10r + (-5r + 25r2) = 0

Combine like terms: -10r + -5r = -15r
-10 + -15r + 25r2 = 0

Solving
-10 + -15r + 25r2 = 0

Solving for variable 'r'.

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

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

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

Simplifying
-2 + -5r = 0

Solving
-2 + -5r = 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 + -5r = 0 + 2

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

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

Divide each side by '-5'.
r = -0.4

Simplifying
r = -0.4
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

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

Simplifying
r = 1
Solution
r = {-0.4, 1}