r(r+5)(r-7)=0

Solution for r(r+5)(r-7)=0 equation:

Simplifying
r(r + 5)(r + -7) = 0

Reorder the terms:
r(5 + r)(r + -7) = 0

Reorder the terms:
r(5 + r)(-7 + r) = 0

Multiply (5 + r) * (-7 + r)
r(5(-7 + r) + r(-7 + r)) = 0
r((-7 * 5 + r * 5) + r(-7 + r)) = 0
r((-35 + 5r) + r(-7 + r)) = 0
r(-35 + 5r + (-7 * r + r * r)) = 0
r(-35 + 5r + (-7r + r2)) = 0

Combine like terms: 5r + -7r = -2r
r(-35 + -2r + r2) = 0
(-35 * r + -2r * r + r2 * r) = 0
(-35r + -2r2 + r3) = 0

Solving
-35r + -2r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-35 + -2r + r2) = 0

Factor a trinomial.
r((-5 + -1r)(7 + -1r)) = 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 '(-5 + -1r)' equal to zero and attempt to solve:

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 3
Set the factor '(7 + -1r)' equal to zero and attempt to solve:

Simplifying
7 + -1r = 0

Solving
7 + -1r = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1r = 0 + -7
-1r = 0 + -7

Combine like terms: 0 + -7 = -7
-1r = -7

Divide each side by '-1'.
r = 7

Simplifying
r = 7
Solution
r = {0, -5, 7}