r^3+24r^2+144r=0

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Solution for r^3+24r^2+144r=0 equation:


Simplifying
r3 + 24r2 + 144r = 0

Reorder the terms:
144r + 24r2 + r3 = 0

Solving
144r + 24r2 + r3 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(144 + 24r + r2) = 0

Factor a trinomial.
r((12 + r)(12 + r)) = 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 '(12 + r)' equal to zero and attempt to solve: Simplifying 12 + r = 0 Solving 12 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + r = 0 + -12 r = 0 + -12 Combine like terms: 0 + -12 = -12 r = -12 Simplifying r = -12

Subproblem 3

Set the factor '(12 + r)' equal to zero and attempt to solve: Simplifying 12 + r = 0 Solving 12 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + r = 0 + -12 r = 0 + -12 Combine like terms: 0 + -12 = -12 r = -12 Simplifying r = -12

Solution

r = {0, -12, -12}

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