-10=r(25r-35)

Solution for -10=r(25r-35) equation:

Simplifying
-10 = r(25r + -35)

Reorder the terms:
-10 = r(-35 + 25r)
-10 = (-35 * r + 25r * r)
-10 = (-35r + 25r2)

Solving
-10 = -35r + 25r2

Solving for variable 'r'.

Reorder the terms:
-10 + 35r + -25r2 = -35r + 35r + 25r2 + -25r2

Combine like terms: -35r + 35r = 0
-10 + 35r + -25r2 = 0 + 25r2 + -25r2
-10 + 35r + -25r2 = 25r2 + -25r2

Combine like terms: 25r2 + -25r2 = 0
-10 + 35r + -25r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 7r + -5r2) = 0

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

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
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
Solution
r = {1, 0.4}