-7(r^2-20r+100)=0

Solution for -7(r^2-20r+100)=0 equation:

Simplifying
-7(r2 + -20r + 100) = 0

Reorder the terms:
-7(100 + -20r + r2) = 0
(100 * -7 + -20r * -7 + r2 * -7) = 0
(-700 + 140r + -7r2) = 0

Solving
-700 + 140r + -7r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-100 + 20r + -1r2) = 0

Factor a trinomial.
7((-10 + r)(10 + -1r)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-10 + r)' equal to zero and attempt to solve:

Simplifying
-10 + r = 0

Solving
-10 + r = 0

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

Add '10' to each side of the equation.
-10 + 10 + r = 0 + 10

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

Combine like terms: 0 + 10 = 10
r = 10

Simplifying
r = 10
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

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

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

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {10, 10}