r(r-3)(r+5)=0

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Solution for r(r-3)(r+5)=0 equation:


Simplifying
r(r + -3)(r + 5) = 0

Reorder the terms:
r(-3 + r)(r + 5) = 0

Reorder the terms:
r(-3 + r)(5 + r) = 0

Multiply (-3 + r) * (5 + r)
r(-3(5 + r) + r(5 + r)) = 0
r((5 * -3 + r * -3) + r(5 + r)) = 0
r((-15 + -3r) + r(5 + r)) = 0
r(-15 + -3r + (5 * r + r * r)) = 0
r(-15 + -3r + (5r + r2)) = 0

Combine like terms: -3r + 5r = 2r
r(-15 + 2r + r2) = 0
(-15 * r + 2r * r + r2 * r) = 0
(-15r + 2r2 + r3) = 0

Solving
-15r + 2r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-15 + 2r + r2) = 0

Factor a trinomial.
r((-5 + -1r)(3 + -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 '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3

Solution

r = {0, -5, 3}

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