4r^3-24r^2=64r

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Solution for 4r^3-24r^2=64r equation:


Simplifying
4r3 + -24r2 = 64r

Reorder the terms:
-24r2 + 4r3 = 64r

Solving
-24r2 + 4r3 = 64r

Solving for variable 'r'.

Reorder the terms:
-64r + -24r2 + 4r3 = 64r + -64r

Combine like terms: 64r + -64r = 0
-64r + -24r2 + 4r3 = 0

Factor out the Greatest Common Factor (GCF), '4r'.
4r(-16 + -6r + r2) = 0

Factor a trinomial.
4r((-2 + -1r)(8 + -1r)) = 0

Ignore the factor 4.

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 '(-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

Subproblem 3

Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8

Solution

r = {0, -2, 8}

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