r(r-2)(r+7)=0

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


Simplifying
r(r + -2)(r + 7) = 0

Reorder the terms:
r(-2 + r)(r + 7) = 0

Reorder the terms:
r(-2 + r)(7 + r) = 0

Multiply (-2 + r) * (7 + r)
r(-2(7 + r) + r(7 + r)) = 0
r((7 * -2 + r * -2) + r(7 + r)) = 0
r((-14 + -2r) + r(7 + r)) = 0
r(-14 + -2r + (7 * r + r * r)) = 0
r(-14 + -2r + (7r + r2)) = 0

Combine like terms: -2r + 7r = 5r
r(-14 + 5r + r2) = 0
(-14 * r + 5r * r + r2 * r) = 0
(-14r + 5r2 + r3) = 0

Solving
-14r + 5r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-14 + 5r + r2) = 0

Factor a trinomial.
r((-7 + -1r)(2 + -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 '(-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

Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0, -7, 2}

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